Related papers: N-expansive Flows
In this paper we study kinematic expansive flows on compact metric spaces, surfaces and general manifolds. Different variations of the definition are considered and its relationship with expansiveness in the sense of Bowen-Walters and…
We define the concept of continuum wise expansive for flows, and we prove that continuum wise expansive flows on compact metric spaces with topological dimension greater than one have positive entropy.
We study continuum-wise expansive flows with fixed points on metric spaces and low dimensional manifolds. We give sufficient conditions for a surface flow to be singular cw-expansive and examples showing that cw-expansivity does not imply…
In light of the rich results of expansiveness in the dynamics of diffeomorphisms, it is natural to consider another notions of expansiveness such as countably-expansive, measure expansive, $N$-expansive and so on. In this paper, we…
In this article we give sufficient conditions for Komuro expansivity to imply the rescaled expansivity recently introduced by Wen and Wen. Also, we show that a flow on a compact metric space is expansive in the sense of Katok-Hasselblatt if…
We introduce the concept of topological expansive flow. We prove that this concept is invariant by topological conjugacy and reduces to expansivity in the compact case. We characterize tiopological expansive flows as rescaling expansive…
We extend the concept of expansive measure \cite{am} defined for homeomorphism to flows. We obtain some properties for such measures including abscense of singularities in the support, aperiodicity, expansivity with respect to time-$T$…
In this article we consider the general problem of translating definitions and results from the category of discrete-time dynamical systems to the category of flows. We consider the dynamics of homeomorphisms and flows on compact metric…
In this paper, we extend a Ma\~n\'e's famous result on expansive homeomorphisms, originally presented in [17], to the setting of flows. Specifically, we provide a complete characterization of minimal expansive flows without fixed points on…
We study two notions of expansiveness for continuous semiflows: expansiveness in the sense of Alves, Carvalho and Siqueira (2017), and an adaptation of positive expansiveness in the sense of Artigue (2014). We prove that if $X$ is a metric…
In this paper we introduce a new notion of expansive flows, which is the combination of expansivity in the sense of Katok and Hasselblatt and kinematic expansivity, named KH-kinematic expansivity. We present new properties of several…
We introduce distinct definitions of local stable/unstable sets for flows without fixed points, namely, kinematic, geometric, and sectionally geometric, and discuss relations between them. We prove the existence of continua with a uniform…
We prove that a flow on a compact surface is expansive if and only if the singularities are of saddle type and the union of their separatrices is dense. Moreover we show that such flows are obtained by surgery on the suspension of minimal…
In this paper, we prove that finite-dimensional topological flows without fixed points and having a countable number of periodic orbits, have the small flow boundary property. This enables us to answer positively a question of Bowen and…
Consider the set $\chi^0_{\mathrm{nw}}$ of non-wandering continuous flows on a closed surface. Then such a flow can be approximated by regular non-wandering flows without heteroclinic connections nor locally dense orbits in…
In this article we consider several forms of expansivity. We introduce two new definitions related with topological dimension. We study the topology of local stable sets under cw-expansive surface homeomorphisms and expansive homeomorphisms…
An attempt is made to extend some of the basic paradigms of dynamics, from the viewpoint of (continuous) flows, to non-metric manifolds.
We give sufficient conditions for a diffeomorphism of a compact surface to be robustly $N$-expansive and cw-expansive in the $C^r$-topology. We give examples on the genus two surface showing that they need not to be Anosov diffeomorphisms.…
In this work we study the problem of positiveness of topological entropy for flows using pointwise dynamics. We show that the existence of a non-periodic nonwandering point of an expansive and non-singular flow with shadowing is a…
In this article we show that the three-dimensional sphere admits {transitive} expansive flows in the sense of Komuro with hyperbolic equilibrium points. The result is based on a construction that allows us to see the geodesic flow of a…