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Galaxy evolution is in transition from an early universe dominated by hierarchical clustering to a future dominated by secular processes. These result from interactions involving collective phenomena such as bars, oval disks, spiral structure, and triaxial dark halos. This paper summarizes a review by Kormendy & Kennicutt (2004) using, in part, illustrations of different galaxies. In simulations, bars rearrange disk gas into outer rings, inner rings, and galactic centers, where high gas densities feed starbursts. Consistent with this picture, many barred and oval galaxies have dense central concentrations of gas and star formation rates that can build bulge-like stellar densities on timescales of a few billion years. We conclude that secular evolution builds dense central components in disk galaxies that look like classical, merger-built bulges but that were made slowly out of disk gas. We call these pseudobulges. Many pseudobulges can be recognized because they have characteristics of disks: (1) flatter shapes than those of classical bulges, (2) correspondingly large ratios of ordered to random velocities, (3) small velocity dispersions, (4) spiral structure or nuclear bars, (5) nearly exponential brightness profiles, and (6) starbursts. These structures occur preferentially in barred and oval galaxies in which secular evolution should be most rapid. Thus a variety of observational and theoretical results contribute to a new paradigm of secular evolution that complements hierarchical clustering.

The secular evolution process, which slowly transforms the morphology of a galaxy over its lifetime, could naturally account for observed properties of the great majority of physical galaxies if both stellar and gaseous accretion processes are taken into account. As an emerging paradigm for galaxy evolution, its dynamical foundation had been established in the past few years, and its observational consequences are yet to be fully explored. The secular evolution picture provides a coherent framework for understanding the extraordinary regularity and the systematic variation of galaxy properties along the Hubble sequence.

Planet crossing orbits give rise to mathematical singularities that make it not possible to apply the classical averaging principle to study the qualitative evolution of Near Earth Asteroids (NEAs). Recently this principle has been generalized to deal with crossings in a mathematical model with the planets on circular coplanar orbits. More accuracy is needed to compute the averaged evolution of planet crossing orbits for different purposes: computing reliable crossing times for the averaged motion, writing more precise proper elements and frequencies for NEAs, etc. In this paper we present the generalization of the averaging principle using a model where the eccentricity and the inclination of the planets are taken into account.

We present calculations of the long-term evolution of CVs which include the influence of nova outbursts. In particular we investigate the consequences of the discontinuous mass loss due to recurring outburst events and the effects of frictional angular momentum loss (FAML), i.e. the interaction of the expanding nova envelope with the secondary. We show that a description assuming continuous mass loss — averaged over a complete nova cycle - is applicable for determining the mean mass transfer rate and the secular evolution both with and without FAML. Between two subsequent outbursts, deviations from the mean evolution depend on the strength of FAML and on the mass ejected during the outburst. Formally FAML is a consequential angular momentum loss [1] and therefore increases the mean mass transfer rate by pushing the systems closer to mass transfer instability. Depending on the actual strenghth of FAML the long-term evolution of CVs could be significantly different from the standard model predictions.

Today we have numerous evidences that spirals evolve dynamically through various secular or episodic processes, such as bar formation and destruction, bulge growth and mergers, sometimes over much shorter periods than the standard galaxy age of 10-15 Gyr. This, coupled to the known properties of the Hubble sequence, leads to a unique sense of evolution: from Sm to Sa. Linking this to the known mass components provides new indications on the nature of dark matter in galaxies. The existence of large amounts of yet undetected dark gas appears as the most natural option. Bounds on the amount of dark stars can be given since their formation is mostly irreversible and requires obviously a same amount of gas.

Recent ground-based photometric investigations suggest that central regions of late-type spirals are closely coupled to the inner disk and probably formed via secular evolution. Evidence presented in support of this model includes the predominance of exponential bulges, the correlation of bulge and disk scale lengths, blueness of the bulge and small differences between bulge and central disk colors, detection of spiral structure into the core, and rapid rotation. Recent HST observations show that our own bulge and that of M31, M32, and M33 probably harbor both an old and intermediate-age populations in agreement with models of early collapse of the spheroid plus gas transfer from the disk. Secular evolution provides a mechanism to build-up central regions in late-type spirals; mergers or accretion of small satellites could explain the brighter, kinematically distinct bulges of Sa's and SO's.

The possible importance of the reaction of a low-mass star to external irradiation for the long-term evolution of compact binaries has been noted only rather recently; first in the context of the evolution of low-mass X-ray binaries (e.g. Podsiadlowski 1991; Harpaz h Rappaport 1991; Frank, King & Lasota 1992; Hameury et al. 1993) and subsequently by Ritter, Zhang & Kolb (1995a,b, hereafter RZK) also for the evolution of cataclysmic variables (CVs). Based on a simple model for describing the reaction of a low-mass star to irradiation RZK showed that CVs can be dynamically unstable against irradiation-induced mass transfer and that, as a consequence of this, mass transfer could occur via cycles in which phases of high, irradiation-enhanced mass transfer alternate with phases of little or no mass transfer. The occurrence of such mass transfer cycles in CVs was subsequently discussed from a more general point of view by King (1995) and King et al. (1995). Whereas the possibility of mass transfer cycles in CVs is now fully recognised, the question as to which systems can undergo such cycles and which cannot has not yet been addressed in detail. It is the purpose of this contribution to provide at least a partial answer to this question.

We investigate to what extent the high mean mass of the white dwarfs in cataclysmic binaries is consequence of selection effects introduced through flux limitation of the observations. In particular, we present first results of new computations in which we correct an error and relax a number of simplifying assumptions made in earlier computations by Ritter and Burkert (1986), and Ritter and Ozkan (1986).

Three ways have been proposed to make elliptical galaxies: cooling by gas dynamical processes at late epochs, Compton cooling at early times and merging. These theories must address a variety of observational constraints, the most severe being the problems of slow rotation and high central phase densities. I look at some aspects of all three theories with particular attention to key numerical simulations and observations that can distinguish between the scenarios.

In this paper I discuss schematically a few aspects of the dynamical evolution of spiral galaxies.

We have adapted the N-body code of Van Albada (1982) to study the secular evolution of a hot collisionless stellar component (E galaxy or galactic bulge) due to slow changes in another component of the same galaxy. Our equilibrium starting model is a non-rotating triaxial ellipsoid with axial ratios 1.3:1.4:2.0; the effects of the “other component” are then simulated by various simple means.

In 1961 Kazimirchak-Polonskaya (1961a, 1961b) published comprehensive reviews of all investigations on the dynamics of cometary orbits as well as on close approaches of the short-period comets with Jupiter for the time span covering 1770–1960 and for the first time put forward the basic problems of cometary astronomy from the standpoint of celestial mechanics. Chebotarev (1971) pointed out that “these reviews, supplemented with extensive references, can serve as a valuable manual for all researchers of cometary motions”.

The basic binary parameters (masses, system dimensions) of all cataclysmic variables are essentially identical, but there is a great variety in the outburst behaviour. Since there is no evident physical reason for this, it is suggested that nova and dwarf nova variability are periodically repeating states of activity of the same binary. After the nova eruption first follows a postnova state (very low disc mass), later the dwarf nova states BV Pup, U Gem and Z Cam (slowly increasing disc mass and outburst frequency, finally standstills), and finally the UX UMa state (permanent standstill) which is terminated by a new nova outburst. The mass of the disc increases continuously during this cycle. Also the mean mass transfer and accretion rates vary slowly from 1018 g s−1 at beginning and end of the cycle to 1016 g s−1 at mid-cycle, as a U Gem star. The nova outburst is understood in terms of a thermonuclear runaway near the surface of the white dwarf, the dwarf nova outburst is due to intermittent accretion of gas which was accumulated in the outer disc during quiescence (several arguments in favor of this model are given). The time interval between consecutive nova outbursts is of the order of 105 years. The secular evolution of a cataclysmic binary is characterized by a period decrease from 10h to 1h5 in a time scale of 1010 years. The star probably passes the period gaps in the ultra-short period domain in form of no-contact configurations.

We study the secular evolution of the orbit described by a meteoric particle moving under the influence of planetary perturbations and the Poynting-Robertson effect. Using a simplified model, this study is made with only one disturbing planet. We present preliminary results on the long-term variation of the osculating elements of the orbit.

Simulations and observations of galactic bars suggest they do not commonly evolve into bulges, although it is possible that the earliest bars formed bulges long ago, when galaxies were smaller, denser, and had more gas. The most highly evolved of today's bars may become lenses over a Hubble time. Most galaxies in the early Universe are extremely clumpy, with 10^8-10^9 Msun blue clumps that resemble in color and magnitude the isolated field objects nearby. The presence of blue and irregular bars at high redshift suggests that some bars formed primarily in the gas phase accompanied by giant starbursts, rather than in pure stellar disks like most models. Secular and non-secular processes that cause galaxies to evolve are summarized.