659 research outputs found
Isolated sets, catenary Lyapunov functions and expansive systems
It is a paper about models for isolated sets and the construction of special
hyperbolic Lyapunov functions. We prove that after a suitable surgery every
isolated set is the intersection of an attractor and a repeller. We give linear
models for attractors and repellers. With these tools we construct hyperbolic
Lyapunov functions and metrics around an isolated set whose values along the
orbits are catenary curves. Applications are given to expansive flows and
homeomorphisms, obtaining, among other things, a hyperbolic metric on local
cross sections for an arbitrary expansive flow on a compact metric space
Lyapunov functions via Whitney's size functions
In this paper we present a technique for constructing Lyapunov functions
based on Whitney's size functions. Applications to asymptotically stable
equilibrium points, isolated sets, expansive homeomorphisms and continuum-wise
expansive homeomorphisms are given
Partially Expansive Homeomorphisms
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 of three-manifolds. The problem of -stable expansivity is
also considered
Lipschitz perturbations of expansive systems
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
perturbations with respect to a hyperbolic metric. We also study the
relationship between Lipschitz topologies and the topology on smooth
manifolds
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