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This paper provides certain computations with transfer associated with projective bundles of \mathrm {Spin} vector bundles. One aspect is to revise the proof of the main result of [Trans. Amer. Math. Soc.349 (1997), pp. 4385-4399] which says that all fourfold products of the Ray classes are zero in symplectic cobordism. [ABSTRACT FROM AUTHOR]

In this paper, we construct a partially hyperbolic skew-product diffeomorphism on 𝕋3, which is accessible and chain transitive, but not transitive. [ABSTRACT FROM AUTHOR]

Let Diffrm(M) be the set of Cr volume-preserving diffeomorphisms on a compact Riemannian manifold M (dimM ≥ 2). In this paper, we prove that the diffeomorphisms without zero Lyapunov exponents on a set of positive volume are C1 dense in Diffrm(M), r ≥ 1. We also prove a weaker result for symplectic diffeomorphisms Symrω(M), r ≥ 1 saying that either the symplectic diffeomorphism f is partially hyperbolic or C1 arbitrarily close to f in Symrω(M), there is a diffeomorphism g ϵ Symrω(M) without zero Lyapunov exponents on a set with positive volume. [ABSTRACT FROM AUTHOR]

Under the relation of 0-concordance, the set of knotted 2-spheres in S^4 forms a commutative monoid \mathcal {M}_0 with the operation of connected sum. Sunukjian [Int. Math. Res. Not. IMRN 17 (2015), pp. 7950–7978] has recently shown that \mathcal {M}_0 contains a submonoid isomorphic to \mathbb {Z}^{\ge 0}. In this note, we show that \mathcal {M}_0 contains a submonoid isomorphic to (\mathbb {Z}^{\ge 0})^\infty. Our argument relates the 0-concordance monoid to linear independence of certain Seifert solids in the spin rational homology cobordism group. [ABSTRACT FROM AUTHOR]

We prove a version of Myers-Steenrod's theorem for Finsler manifolds under the minimal regularity hypothesis. In particular we show that an isometry between Ck,α-smooth (or partially smooth) Finsler metrics, with k +α > 0, k ∈ N ∪{0}, and 0 = α = 1 is necessarily a diffeomorphism of class Ck+1,α. A generalization of this result to the case of Finsler 1-quasiconformal mapping is given. The proofs are based on the reduction of the Finslerian problems to Riemannian ones with the help of the Binet-Legendre metric. [ABSTRACT FROM AUTHOR]

Let $f$ be a diffeomorphism of a closed $C^infty $ manifold $M$. In this paper, we introduce the notion of the $C^1$-stable specification property for a closed $f$-invariant set $Lambda $ of $M$, and we prove that $f_{|Lambda }$ satisfies a $C^1$-stable specification property if and only if $Lambda $ is a hyperbolic elementary set. As a corollary, the $C^1$-interior of the set of diffeomorphisms of $M$ satisfying the specification property is characterized as the set of transitive Anosov diffeomorphisms. [ABSTRACT FROM AUTHOR]

In this paper we study a nonlinear periodic problem driven by the ordinary scalar p-Laplacian and with a Carathéodory nonlinearity. We establish the existence of at least two nontrivial solutions. Our approach is variational based on the smooth critical point theory and using the ``Second Deformation Theorem". [ABSTRACT FROM AUTHOR]

In this paper, we shall prove that for any integer $n>0$, 1) a handlebody of genus 2 contains a separating incompressible surface of genus $n$, 2) there exists a closed 3-manifold of Heegaard genus $2$ which contains a separating incompressible surface of genus $n$. [ABSTRACT FROM AUTHOR]

A famous result of Zimmermann-Huisgen, Hille and Reineke asserts that any projective variety occurs as a quiver Grassmannian for a suitable representation of some wild acyclic quiver. We show that this happens for any wild acyclic quiver. [ABSTRACT FROM AUTHOR]

Abstract. Shub and Wilkinson and Ruelle and Wilkinson studied a class of volume preserving diffeomorphisms on the three dimensional torus that are stably ergodic. The diffeomorphisms are partially hyperbolic and admit an invariant central foliation of circles. The foliation is not absolutely continuous; in fact, Ruelle and Wilkinson established that the disintegration of volume along central leaves is atomic. We show that in such a class of volume preserving diffeomorphisms the disintegration of volume along central leaves is a single delta measure. We also formulate a general result for conservative three dimensional skew product like diffeomorphisms on circle bundles, providing conditions for delta measures as disintegrations of the smooth invariant measure. [ABSTRACT FROM AUTHOR]

We study the specification property for partially hyperbolic dynamical systems. In particular, we show that if a partially hyperbolic diffeomorphism has two saddles with different indices, and the stable manifold of one of these saddles coincides with the strongly stable leaf, then it does not satisfy the specification property. [ABSTRACT FROM AUTHOR]

We investigate contrasting behaviours emerging when studying foliations on non-metrisable manifolds. [ABSTRACT FROM AUTHOR]

We construct, for each irrational number α, a minimal C¹-diffeomorphism of the circle with rotation number a which admits a measurable fundamental domain with respect to the Lebesgue measure. [ABSTRACT FROM AUTHOR]

For commuting smooth quasiperiodically forced circle diffeomorphisms, we show that if the base frequencies and the fibred rotation numbers jointly satisfy some simultaneous Diophantine condition and if the diffeomorphisms are in some C∞ neighborhood of the corresponding rotations, then they are simultaneously C∞-linearizable. [ABSTRACT FROM AUTHOR]

Let M be a closed manifold and f be a diffeomorphism on M. We show that if f has a nontrivial dominated splitting TM = E ⊕ F, then f cannot be minimal. The proof mainly uses Mañé's argument and Liao's selecting lemma. [ABSTRACT FROM AUTHOR]