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We study certain one-parameter families of partially hyperbolic maps of skew-product type generating so-called porcupine-like horseshoes. Such sets are topologically transitive and semiconjugate to the shift map in two symbols. They exhibit a very rich fiber structure characterized by the fact that the set is the disjoint union of two dense and uncountable subsets with opposite behavior: corresponding spines (preimage of a sequence by the semiconjugation) are nontrivial and trivial, respectively, that is, the semiconjugation is noninjective and injective, respectively. We will study the bifurcation process of creation and annihilation of nontrivial spines as the parameter t evolves. In particular, we focus on the Hausdorff dimension of these subsets of . This study illustrates the richness of the process.

We give an explicit family of polynomial maps called center unstable H\'enon-like maps and prove that they exhibits blenders for some parametervalues. Using this family, we also prove the occurrence of blenders near certain non-transverse heterodimensional cycles under high regularity assumptions. The proof involves a renormalization scheme along heteroclinic orbits. We also investigate the connection between the blender and the original heterodimensional cycle.

We consider diffeomorphisms $f$ with heteroclinic cycles associated to saddles $P$ and $Q$ of different indices. We say that a cycle of this type can be stabilized if there are diffeomorphisms close to $f$ with a robust cycle associated to hyperbolic sets containing the continuations of $P$ and $Q$. We focus on the case where the indices of these two saddles differ by one. We prove that, excluding one particular case (so-called twisted cycles that additionally satisfy some geometrical restrictions), all such cycles can be stabilized., Comment: 31 pages, 9 figures

Much effort over many years has been devoted to the reform of the teaching of physics. This has led to many new and imaginative approaches in the content and delivery of material. Great strides have been made in the delivery, and the content has been continually supplemented. However, attempts to modernize the basic structure of the presentation have faced resistance, and the majority of introductory physics textbooks in wide adoption today have a general structure that has changed little in over 60 years. Thus, in comparison to biology, chemistry, geology, etc, physics is unique in that its introductory course is not a survey of the current status of the field. In an attempt to circumvent this problem in a tractable way, we have developed a qualitative front-end course designed to create a 21st century perspective that can be embedded into the beginning of a standard introductory physics sequence.

In atomic systems for which the total oscillator strength of excitations from the ground state is dominated by the transition to the lowest resonance level, the f-sum rule provides a bracketing inequality connecting the lifetime τ of that level to the dipole polarizability αd. This relationship has been used previously to deduce αd from τ. It is shown here that improved spectroscopic accuracies now permit this procedure to be inverted, with τ deduced from a value for αd obtained spectroscopically using the core polarization model. A similar quantitative relationship exists connecting the nonadiabatic correlation factor β to τ, and thus also to αd. The method is applied to a recent measurement of αd for Kr6+ to obtain the values τ(4s4p1P1) = 0.096 ± 0.003 ns and β(Kr6+) = 1.71 ± 0.03a50. It is shown that the use of this method to make precision lifetime determinations for a small number of ions in an isoelectronic sequence permits the exploitation of observed semiempirical regularities to specify the lifetimes of all ions in that sequence.

Much progress has been made in the measurement of oscillator strengths in neutral and singly-ionized atoms, providing a database for use in important applications. However, for multiply-charged ions, measured data for oscillator strengths are almost exclusively limited to low-lying unbranched transitions. Although extensive measurements of ionic lifetimes exist, the lack of branching fraction measurements in multiply-charged ions prevents these data from being converted to oscillator strengths. A significant factor leading to this deficiency involves the lack of adequate line intensity calibration standards in the vacuum ultraviolet spectral region 2000‐400 A. Here we review the interrelationships connecting these rate parameters, indicate some of the important applications for which they are needed, describe the experimental limitations that currently exist, and suggest possible methods for extending these measurements below 1000 A.

The decays of the 2p J = 1/2 and J = 3/2 levels of Li-like ions and of the 2s2p 1,3 P o levels of Be-like ions can be used as simple-atom test beds for lifetime measurements and for the development of accurate calculations of the transition rates. We have summarized and filtered the experimental data in order to obtain consistent data sets and isoelectronic trends that can be compared to theoretical predictions. The graphical presentation of line strength data enables direct comparison and evaluation of the merit of data along extended isoelectronic sequences. From this, the precision that is necessary in future meaningful experiments can be deduced.

There are significant differences in the structures of course presentations of classical mechanics and quantum mechanics, but also essential links that connect the two approaches. A large part of the differences in approach do not involve quantization, but rather the traditional use of instantaneous values to describe macroscopic objects and position probability densities to describe microscopic objects. A pedagogic reformulation of the classical problem to bridge this gap is presented here. The method is numerical in nature, but for illustrative purposes it is herein applied to two specific cases for which analytic solutions also exist, the Kepler–Coulomb potential and the isotropic harmonic oscillator. Using this approach, classical systems can be examined in the presence of perturbations in the same way as is used in quantum mechanics courses. Semiclassical quantization can also be introduced to extend the connection to a quantum-mechanical treatment.

The study of atomic and ionic lifetimes and transition probabilities has undergone a period of intense activity, facilitated largely by the application of the technique of Beam-Foil Spectroscopy. This area is now a mature field of study (having been pursued for 40 years), and has provided much new data, elucidated fundamental atomic processes, and furthered applications in many fields. However, technical advances have now broadened the field to permit new types of measurements of unprecedented accuracy and scope. Thus, this occasion offers an appropriate opportunity to review some of the successful applications of the method, to survey the present state of knowledge, and to indicate areas that hold promise for future research.

Semiempirical methods are used to characterize and parametrize the effects of intermediate coupling and configuration interaction on the energy levels of the 3s3p, 3p2 and 3s3d configurations for ions in the Mg isoelectronic sequence. These parametrizations are then used to predict the branching fractions for the 3s3p–3p2 and 3s3p–3s3d transition arrays. The predictions are compared with the MCHF calculations for S V and Fe XV, and good agreement is obtained. The application of this method to deduce transition probabilities and oscillator strengths from lifetime measurements is discussed.

We study diffeomorphisms of a closed connected manifold whose non-wandering set has a non-empty interior and conjecture that C1-generic diffeomorphisms whose non-wandering set has a non-empty interior are transitive. We prove this conjecture in three cases: hyperbolic diffeomorphisms, partially hyperbolic diffeomorphisms with two hyperbolic bundles, and tame diffeomorphisms (in the first case, the conjecture is folklore; in the second one, it follows by adapting the proof in Brin (1975 Topological transitivity of a certain class of dynamical systems, and flows of frames on manifolds of negative curvature Funct. Anal. Appl. 9 9–19)).We study this conjecture without global assumptions and prove that, generically, a homoclinic class with non-empty interior is either the whole manifold or else accumulated by infinitely many different homoclinic classes. Finally, we prove that, generically, homoclinic classes and non-wandering sets with non-empty interiors are weakly hyperbolic (the existence of a dominated or a volume hyperbolic splitting).

In this paper we study one-parameter families (f?)?[?1,1] of two-dimensional diffeomorphisms unfolding critical saddle-node horseshoes (say at ? = 0) such that f? is hyperbolic for negative ?. We describe the dynamics at some isolated secondary bifurcations that appear in the sequel of the unfolding of the initial saddle-node bifurcation. We construct two classes of open sets of such arcs. For the first class, we exhibit a collection of parameter intervals In, In?(0,1], converging to the saddle-node parameter, In?0, such that the topological entropy of f? is a constant hn in In and hn is an increasing sequence. So, for parameters in In, the topological entropy is upper bounded by the entropy of the initial saddle-node diffeomorphisms. This illustrates the following intuitive principle: a critical cycle of an attracting saddle-node horseshoe is a destroying dynamics bifurcation. In the second class, the entropy of f? does not depend monotonically on the parameter ?. Finally, when the saddle-node horseshoe is not an attractor, we prove that the entropy may increase after the bifurcation.

Recent studies of the Si and Ge isoelectronic sequences have shown that branching fractions within the ns2np2–ns2np(n + 1)s supermultiplets are accurately described by a semiempirical model that uses spectroscopic energy level data to characterize intermediate coupling. It was also recently shown that a similar model applied to alkaline-earthlike ns2–nsnp transitions can be advantageously generalized to include the effects of spin-other-orbit interaction and differences between the singlet and triplet radial wave functions. These two formalisms are combined, extended, and applied here to obtain a predictive systematization of branching fractions for the 5s25p2–5s25p6s supermultiplet of the ions Sn I–Cs VI in the Sn sequence.

Branching fractions and relative transition probabilities are predicted for the ns2-nsnp and nsnp-nsnd supermultiplets in Ga II, In II and Tl II through a data-based systematization of measured lifetime and spectroscopic energy level data. A formalism is used that parametrizes the effects of Coulomb exchange, spin-orbit and spin-other-orbit interactions, and differences between the radial wave functions of the singlet and triplet states to deduce effective intermediate coupling amplitudes. Connections between singlet and triplet lifetimes and among triplet lifetimes are examined and predictions are made where data do not currently exist.

Accelerator mass spectrometry (AMS) is a highly sensitive method for counting atoms. It is used for detecting very low concentrations of both radionuclides and stable nuclides. The main advantages of AMS compared to conventional radiometric methods are the use of smaller samples (mg size) and shorter measuring times (less than one hour). In AMS, rare isotopes from a sample material placed in the ion source of an electrostatic tandem accelerator are measured by counting individual atoms with nuclear detection techniques after acceleration to energies in the MeV range. A dramatic improvement in background rejection for AMS systems has, in the best cases, led to a 108 increase in sensitivity for isotope ratio measurements compared to the older technique of mass spectrometry. In this report some current applications of the AMS technique at the Lund Pelletron accelerator, as well as the recent improvements of the Lund system, are presented.

The use of lifetime measurements for the specification of transition probabilities along isoelectronic sequences is hindered by the fact that virtually no branching fraction measurements exist for multiply charged ions. Part of the reason for this lies in the lack of calibration standards for intensity as a function of wavelength in the ultraviolet region. It has been shown that transitions of the form ns2np2 - ns2npn´s in Si I and Ge I are virtually free of configuration interaction, hence their branching fractions can be accurately predicted from intermediate coupling amplitudes deduced from measured spectroscopic energy level data. Reported here is the extension of these semiempirical methods to the ions P II, S III, Cl IV and Ar V in the Si sequence and As II, Se III and Br IV in the Ge sequence. This provides a set of branching fractions that can both specify transition probability rates from lifetime measurements for these ions, and serve as a set of lines of known relative intensities for use in the calibration of detection apparatus in the UV region.

The extensive arc emission measurements of transition probabilities by Corliss and Bozman are known to contain errors due to flaws in the determination of level populations in the source. However, if no similar errors were present in the photometric calibration, then branching fractions from the same upper level deduced from these measurements should be valid. It is shown that the branching fractions for the transitions in Si I, Ge I, Sn I and Pb I can be accurately estimated using intermediate coupling amplitudes obtained from spectroscopic data, and thus provide a test of the validity of these measurements. The results of Corliss and Bozman are examined in the context of comparisons with these estimated values and with other measurements, and it is demonstrated that branching fractions from the same upper level obtained from these data can be quite reliable.

Lifetimes of several 2p3s, 2p3p and 2p3d levels in singly ionized boron, B II, have been determined by means of beam–foil spectroscopy and theoretical calculations, using the superposition-of-configurations (SOC) program of Cowan. These doubly-excited terms which lie close to the first ionization limit of B II make radiative transitions to the singly excited system. For a few autoionizing 2p3l levels we have calculated excitation energies and decay rates. The theoretical and experimental data are generally in very good agreement.

A relativistic extension is made of methods by which intermediate coupling amplitudes are deduced from measured energy levels and combined with measured lifetimes to obtain transition probabilities within a multiplet between two pure configurations. A procedure for incorporating the relativistic j-dependence of the radial transition integral into the empirical data reduction is presented and applied to the isoelectronic formulation of the 2s2-2s2p transitions in the Be sequence and the 6s26p2-6s26p7s transitions in the Pb sequence.

We study the unfolding of heterodimensional cycles (i.e. cycles containing periodic points with different indices). Given any we construct an open set of arcs that unfold generically a heterodimensional cycle so that the relative measure at the bifurcation value of the set of parameter corresponding to -stable diffeomorphisms is bigger than . On the other hand, the bifurcation value is not a point of full density of hyperbolic dynamics.

Lifetimes are reported for the , and levels in Hg-like Tl II, measured using beam-foil excitation. The values obtained were , , , and . Isoelectronic trends for line strengths of the resonance and intercombination transitions are studied through comparisons with earlier measurements for Hg I - Bi IV.

New observations of the 3s23p 2P–3s3p2 4P intercombination transitions in Al-like ions have been made for Cl V from spark spectra recorded at Lund and for Kr XXIV and Mo XXX from spectra obtained at the JET tokamak. The new results have been combined with other identifications of these transitions along the sequence and empirically systematized and compared with theoretical calculations. A set of smoothed and interpolated values for the excitation energies of the 3s3p2 4P levels in P III-Mo XXX is presented.

Measured lifetime data for the 2s 21 S 0 -2s2p 1;3 P1 resonance and intercombination lines in the Be isoelectronic sequence are critically evaluated, and jointly systematized using effective singlet-triplet-reduced line strengths Sr. The data are examined together with recent theoretical predictions in the linearizing exposition Z 2 Sr D SHCB=.Z C/ and the high-Z trend is compared with the corresponding hydrogenic limit. Smoothed and interpolated predictions are presented for Z 6 54.

This paper reports an extended experimental investigation, using the beamfoil technique, of the intensity ratio of the fine-structure components in the 3s23p 2P1/2,3/2–3s3p2 2S1/2 and 2P1/2 resonance transitions along the Al I isoelectronic sequence. These intensity ratios are strongly influenced by cancellation/enhancement effects arising from spin-orbit induced level mixings, and are thus sensitive probes of the detailed atomic structure. New data are given for Si II, P III, S IV, K VII, Sc IX, Fe XIV and Ni XVI. Together with previous experimental results this comprehensive isoelectronic study reveals significant and systematic deviations from theoretical predictions.

We construct an open set A of arcs of diffeomorphisms bifurcating through the creation of heterodimensional cycles (i.e. there are points in the cycle having different indices) being robustly nonhyperbolic after the unfolding of the cycle: every diffeomorphism is not hyperbolic. We also prove that the arcs in A exhibit cycles persistently. Finally, for generic arcs in A and for a full (Lebesgue) set of parameters values we prove that the resulting nonwandering set is transitive and local maximal.

Lifetime measurements using beam foil techniques for the $5s5p^{2}$ $^{2}D_{3/2,5/2}$ levels in Sn II are presented. The resulting oscillator strengths for transitions at 1699.4, 1831.8 and 1811.2 \AA{} are reported. We also studied these levels with multi-configuration Dirac Hartree-Fock (MCDHF) calculations using a development version of the GRASP2K package. Our experimental and theoretical results are compared with other available studies.

We have observed radiation from highly charged molybdenum ions in the JET tokamak plasmas. Spectra were recorded in the wavelength range 70-110 Angstrom, resulting in the classification of 15 new n = 3. Deltan = 0 transitions in Mo XXIV-Mo XXVIII.

Beam-foil lifetime data on the intercombination line 4s2 1S0-4s4p 3P10 in the Zn-like ions are reviewed and compared to various theoretical predictions. These predictions spread by about a factor of three. After massive corrections for experimental term energies and singlet-triplet splittings, this spread is reduced to a much narrower band, and most of the predictions then agree with the experimental lifetime findings and with the trend predicted by calculations which explicitly take core polarization into account. A screening parameterization of the experimental lifetime and term structure data can then be used to represent singlet and triplet resonance level lifetimes by a single, common curve.

The use of data-based semiempirical methods to produce high precision predictions and systematizations along isoelectronic sequences is discussed and applied to several examples. Applications include: studies of trends in the lifetimes of resonance transitions in alkali-like isoelectronic sequences; the combined systematization of spin-allowed and spin-forbidden transition probabilities in alkaline earth-like and inert gas-like isoelectronic sequences; the use of screening and quantum defect parametrizations to predict ionization potentials for the Be sequence.

The authors study arcs of diffeomorphisms that bifurcate through the creation of a nonconnected heterodimensional cycle. They exhibit two open sets of such arcs; in the first one, after the bifurcation, the set of parameter values for which the corresponding diffeomorphism is stable (stable set) is empty, in the second one Omega -stability has some degree of prevalence, i.e. the relative measure of the Omega -stable set is bounded away from zero.

Studies of the useful lifetime of 2-5 µg cm−2 carbon stripper foils have been made using 225 keV heavy ion beam bombardment. The foils were self supporting and were mounted both in a standard and a tension-slackened manner. In determining the quality of the foil during ion bombardment several techniques were used, in particular beam-foil spectroscopy. Here the intensity of the light emitted by the foil-emergent beam was measured as a function of bombardment time. The measured lifetime before foil failure for standard foils was found to agree well with a semiempirical model proposed by Auble and Galbraith, and the slackened foils exhibited usable lifetimes 3-4 times longer than the normal foils. The properties of ordinary and slackened foils were compared under realistic conditions. It is concluded that the slackened foils are very well suited for studies of atomic spectra and meanlives of excited states using beam foil excitation methods.

A method is presented that accounts for the effects of singlet-triplet mixing in measured lifetimes of resonance and intercombination lines in alkaline-earthlike and inert-gaslike isoelectronic sequences. The method uses measured lifetimes and spectroscopic energy levels as its only inputs, and yields mixing-reduced line strength factors that can be isoelectronically linearized for precision interpolation, extrapolation, and smoothing. The method is applied to predictively systematize lifetimes in the Be, Mg and Ne iso-electronic sequences.

Lifetimes are reported for the twelve 4d95p fine structure levels of Cd III, measured using beam-foil excitation. Isoelectronic trends are studied through comparisons with earlier measurements for Ag II (Irving R E et al 1995 Physica Scripta 51 351).