相关论文: Homoclinic tangency and variation of entropy
We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by one which is essentially…
We prove here that in the complement of the closure of the hyperbolic surface diffeomorphisms, the ones exhibiting a homoclinic tangency are C^1 dense. This represents a step towards the global understanding of dynamics of surface…
We show that any diffeomorphism of a compact manifold can be C1 approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.
We consider a $C^1$ neighborhood of the time-one map of a hyperbolic flow and prove that the topological entropy varies continuously for diffeomorphisms in this neighborhood. This shows that the topological entropy varies continuously for…
We prove that every C1 diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant. Consequently, such diffeomorphisms satisfy Shub's entropy conjecture: the entropy is bounded from below…
We prove that any diffeomorphism of a compact manifold can be C^1-approximated by a diffeomorphism which exhibits a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by a diffeomorphism which is partially…
We consider partially hyperbolic diffeomorphisms $f$ with a one-dimensional central direction such that the unstable entropy exceeds the stable entropy. Our main result proves that such maps have a finite number of ergodic measures of…
We consider partially hyperbolic diffeomorphisms on compact manifolds where the unstable and stable foliations stably carry some unique non-trivial homologies. We prove the following two results: if the center foliation is one dimensional,…
The aim of this work is to study a kind of refinement of the entropy conjecture, in the context of partially hyperbolic diffeomorphisms with one dimensional central direction, of d-dimensional torus. We start by establishing a connection…
Let $f$ be a $C^{1}$ diffeomorphism on a compact manifold $M$ admitting a partially hyperbolic splitting $TM=E^{s}\oplus_{\prec} E^{1}\oplus_{\prec} E^{2}\cdots \oplus_{\prec}E^{l}\oplus_{\prec} E^{u}$ where $E^{s}$ is uniformly…
A diffeomorphism $f$ has a $C^1$-robust homoclinic tangency if there is a $C^1$-neighbourhood $\cU$ of $f$ such that every diffeomorphism in $g\in \cU$ has a hyperbolic set $\La_g$, depending continuously on $g$, such that the stable and…
In this paper, we consider certain partially hyperbolic diffeomorphisms with center of arbitrary dimension and obtain continuity properties of the topological entropy under $C^1$ perturbations. The systems considered have subexponential…
We consider $C^r$ ($r\geqslant 1$) diffeomorphisms $f$ defined on manifolds of dimension $\geqslant 3$ with homoclinic tangencies associated to saddles. Under generic properties, we show that if the saddle is homoclinically related to a…
In this paper, we investigate the relationship between chaos and homoclinic orbits from a quantitative perspective. Let f be a C^r diffeomorphism (r > 1) on a compact Riemannian manifold preserving an ergodic hyperbolic measure. We show…
We prove the topological entropy remains constant inside the class of partially hyperbolic diffeomorphisms of $\mathbb{T}^d$ with simple central bundle (that is, when it decomposes into one dimensional sub-bundles with controlled geometry)…
The aim of this paper is twofold. First, we introduce standard blenders (special hyperbolic sets) and their variations, and prove their fundamental properties on the generation of $C^1$-robust tangencies. In particular, these blenders…
The (measure-theoretical) entropy of a diffeomorphism along an expanding invariant foliation is the rate of complexity generated by the diffeomorphism along the leaves of the foliation. We prove that this number varies upper…
We prove that every $C^1$ three-dimensional flow with positive topological entropy can be $C^1$ approximated by flows with homoclinic orbits. This extends a previous result for $C^1$ surface diffeomorphisms \cite{g}.
We prove that the $C^3$ diffeomorphisms on surfaces, exhibiting infinitely many sinksnear the generic unfolding of a quadratic homoclinic tangency of a dissipative saddle, can be perturbed along an infinite dimensional manifold of $C^3$…
We show that $C^\infty$ surface diffeomorphisms with positive topological entropy have at most finitely many ergodic measures of maximal entropy in general, and at most one in the topologically transitive case. This answers a question of…