Related papers: Attractors with non-invariant interior

Let $M^n$, $n\geq 3$, be a closed orientable $n$-manifold and $\mathbb{D}_k(M^n;a,b,c)$ the set of axiom A diffeomorp\-hisms $f: M^n\to M^n$ satisfying the following conditions: (1) $f$ has $k\geq 1$ nontrivial basic sets each is either an…

We define a diffeomorphism invariant of smooth 4-manifolds which we can estimate for many smoothings of R^4 and other smooth 4-manifolds. Using this invariant we can show that uncountably many smoothings of R^4 support no Stein structure.…

In this paper we study the geometry of the attractors of holomorphic maps with an irrationally indifferent fixed point. We prove that for an open set of such holomorphic systems, the local attractor at the fixed point has Hausdorff…

There are a least uncountably many diffeomorphism types for open manifolds. Hence the classification problem is extremely difficult. We proceed as follows: We define several uniform structures of proper metric spaces and consider their arc…

Let $M$ be a manifold or (more generally) a locally compact, metrizable ANR. If $K$ is an attractor for a flow in $M$, with basin of attraction $\mathcal{A}(K)$, it is well known that the inclusion $i : K \subseteq \mathcal{A}(K)$ is always…

Let f be a diffeomorphism of a compact finite dimensional boundaryless manifold M exhibiting infinitely many coexisting attractors. Assume that each attractor supports a stochastically stable probability measure and that the union of the…

The use of a diffeomorphism covariant star product enables us to construct diffeomorphism invariant gravities on noncommutative symplectic manifolds without twisting the symmetries. As an example, we construct noncommutative deformations of…

We propose an approach to the attractors of skew products that tries to avoid unnecessary structures on the base space and rejects the assumption on the invariance of an attractor. When nonivertible maps in the base are allowed, one can…

We study the topological properties of attractors of Iterated Function Systems (I.F.S.) on the real line, consisting of affine maps of homogeneous contraction ratio. These maps define what we call a second generation I.F.S.: they are…

We relate the Mather invariant of diffeomorphisms of the (closed) interval to their asymptotic distortion. For maps with only parabolic fixed points, we show that the former is trivial if and only if the latter vanishes. As a consequence,…

This paper refined and introduced some notations (namely attractors, physical attractors, proper attractors, topologically exact and topologically mixing) within the context of relations. We establish necessary and sufficient conditions,…

The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…

We show that robustly transitive endomorphisms of a closed manifolds must have a non-trivial dominated splitting or be a local diffeomorphism. This allows to get some topological obstructions for the existence of robustly transitive…

Let $M$ be a $d\times d$ contracting matrix. In this paper we consider the self-affine iterated function system $\{Mv-u, Mv+u\}$, where $u$ is a cyclic vector. Our main result is as follows: if $|\det M|\ge 2^{-1/d}$, then the attractor…

We present some rigorous results on the absence of a wide class of invariant measures for dynamical systems possessing attractors. We then consider a generalization of the classical nonholonomic Suslov problem which shows how previous…

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…

Attractors of cooperative dynamical systems are particularly simple; for example, a nontrivial periodic orbit cannot be an attractor. This paper provides characterizations of attractors for the wider class of coherent systems, defined by…

We study the problem of persistence of attractors with smooth boundary for a class of set-valued dynamical systems that naturally arise in the context of random and control dynamical systems, as well as in systems modeling the dynamical…

Embedding techniques allow the approximations of finite dimensional attractors and manifolds of infinite dimensional dynamical systems via subdivision and continuation methods. These approximations give a topological one-to-one image of the…

Spectral submanifolds (SSMs) are invariant manifolds of a dynamical system, defined by the property of being tangent to a spectral subspace of the linearized dynamics at a steady state. We show existence, along with certain desirable…