N-expansive flows

@article{Artigue2021NexpansiveF,
  title={N-expansive flows},
  author={Alfonso Artigue and Welington Cordeiro and Maria Jos'e Pac'ifico},
  journal={Topology and its Applications},
  year={2021}
}
We define the concept of $N$-expansivity for flows. We show examples of $N$-expansive flows but not expansive, and we show examples of $CW$-expansive flows but not $N$-expansive for any natural number $N$. 
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References

SHOWING 1-10 OF 29 REFERENCES
Singular Cw-Expansive Flows
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
Continuum-wise expansivity and entropy for flows
We define the concept of continuum-wise expansivity for flows, and we prove that continuum-wise expansive flows on compact metric spaces with topological dimension greater than one have positive
Real-expansive flows and topological dimension
We examine generalizations of R. Mane's results on the topological dimension of spaces supporting an expansive homeomorphism to the case of real-expansive flows. We show that a space supporting a
Robustly N-expansive surface diffeomorphisms
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
N-expansive homeomorphisms with the shadowing property
We discuss the dynamics of $n$-expansive homeomorphisms with the shadowing property defined on compact metric spaces. For every $n\in\mathbb{N}$, we exhibit an $n$-expansive homeomorphism, which is
A generalization of expansivity
We study dynamical systems for which at most $n$ orbits can accompany a given arbitrary orbit. For simplicity we call them $n$-expansive (or positively $n$-expansive if positive orbits are
Kinematic expansive flows
  • A. Artigue
  • Mathematics
    Ergodic Theory and Dynamical Systems
  • 2014
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
N-expansive homeomorphisms on surfaces.
In this paper we study N-expansive homeomorphisms on surfaces. We prove that when f is a 2-expansive homeomorphism defined on a compact boundaryless surface M with non-wandering set Ω(f) being the
Expansive flows of surfaces
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
Measure N-expansive systems
Abstract The N-expansive systems have been recently studied in the literature [6] , [7] , [9] , [14] . Here we characterize them as those homeomorphisms for which every Borel probability measure is
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