Open Access
2017 Isolated sets, catenary Lyapunov functions and expansive systems
Alfonso Artigue
Topol. Methods Nonlinear Anal. 49(1): 21-50 (2017). DOI: 10.12775/TMNA.2016.067


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.


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Alfonso Artigue. "Isolated sets, catenary Lyapunov functions and expansive systems." Topol. Methods Nonlinear Anal. 49 (1) 21 - 50, 2017.


Published: 2017
First available in Project Euclid: 11 April 2017

zbMATH: 1380.37030
MathSciNet: MR3635636
Digital Object Identifier: 10.12775/TMNA.2016.067

Rights: Copyright © 2017 Juliusz P. Schauder Centre for Nonlinear Studies

Vol.49 • No. 1 • 2017
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