Related papers: Inverse periodic shadowing properties

We extend some known results from smooth dynamical systems to the category of Lipschitz homeomorphisms of compact metric spaces. We consider dynamical properties as robust expansiveness and structural stability allowing Lipschitz…

We consider C^r-diffeomorphisms of a compact smooth manifold having a pair of robust heterodimensional cycles where r is a positive integer or infinity. We prove that if certain conditions about the signatures of non-linearities and…

In this paper, we develop the basic theory of the shadowing property for local homeomorphisms of metric locally compact spaces, with a focus on applications to edge shift spaces connected with C*-algebra theory. For the local homeomorphism…

We use the inverse pressure concept to estimate the stable dimension for hyperbolic non-invertible maps which are conformal in the stable fibers. The non-invertible case is different than the diffeomorphism case. In particular we show that…

We study the effects that the constant periodic data condition have on topological entropy of Anosov diffeomorphisms. Under constant periodic data condition we prove that Anosov diffeomorphism has finitely many measures of maximal entropy…

Let $\mathcal{R}$ be a strongly compact $C^2$ map defined in an open subset of an infinite-dimensional Banach space such that the image of its derivative $D_F \mathcal{R}$ is dense for every $F$. Let $\Omega$ be a compact, forward invariant…

We show there is a residual set of non-Anosov $C^{\infty}$ Axiom A diffeomorphisms with the no cycles property whose elements have trivial centralizer. If $M$ is a surface and $2\leq r\leq \infty$, then we will show there exists an open and…

In this article we study some statistical aspects of surface diffeomorphisms. We first show that for a $C^1$ generic diffeomorphism, a Dirac invariant measure whose \emph{statistical basin of attraction} is dense in some open set and has…

We study Hamiltonian diffeomorphisms on symplectic Euclidean spaces that are equal to non-degenerate linear maps at infinity. Under the assumption that there exists an isolated homologically nontrivial fixed point satisfying the twist…

We prove that every factor map between topological flows preserves the standard shadowing property if it is injective except for a closed orbit that shrinks to a singularity. As an application, we construct a $C^\infty$-flow on a…

We study the problem of conjugating a diffeomorphism of the interval to (positive) powers of itself. Although this is always possible for homeomorphisms, the smooth setting is rather interesting. Besides the obvious obstruction given by…

We prove that any C1-stably weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E + F. Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result…

It is known that Morse-Smale diffeomorphisms have the shadowing property; however, the question of whether $C(f)$ also has the shadowing property when $f$ is Morse-Smale remains open and has been resolved only in a few specific…

It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular,…

We prove a very general Weyl-type law for Periodic Floer Homology, estimating the action of twisted Periodic Floer Homology classes over essentially any coefficient ring in terms of the grading and the degree, and recovering the Calabi…

We study shadowing property for a partially hyperbolic diffeomorphism $f$. It is proved that if $f$ is dynamically coherent then any pseudotrajectory can be shadowed by a pseudotrajectory with "jumps" along the central foliation. The proof…

We point out a basic dichotomy between the shadowing and Lipschitz shadowing properties for one-sided shift spaces in two infinite-alphabet frameworks: the classical product-topology model $X\subseteq A^{\mathbb{N}}$ and the compact…

A given self-map $f\colon M\to M$ of a compact manifold determines the sequence $(L(f^n))$ of the Lefschetz numbers of its iterations. We consider its dual sequence $(a_n(f))$ given by the M\"obius inversion formula. The set ${\mathcal…

This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent…

We show that for the generic continuous maps of the interval and circle which preserve the Lebesgue measure it holds for each k $\ge$ 1 that the set of periodic points of period k is a Cantor set of Hausdorff dimension zero and of upper box…