Lyapunov exponents and uniform weak normally repelling invariant sets

Paul Leonard Salceanu, Hal Smith

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

Let M be a compact invariant set contained in a boundary hyperplane of the positive orthant of ℝn for a discrete or continuous time dynamical system defined on the positive orthant. Using elementary arguments, we show that M is uniformly weakly repelling in directions normal to the boundary in which M resides provided all normal Lyapunov exponents are positive. This result is useful in establishing uniform persistence of the dynamics.

Original languageEnglish (US)
Title of host publicationPositive Systems - Proceedings of the third Multidisciplinary International Symposium on Positive Systems
Subtitle of host publicationTheory and Applications, POSTA 2009
Pages17-27
Number of pages11
DOIs
StatePublished - Dec 1 2009
Event3rd Multidisciplinary Symposium on Positive Systems: Theory and Applications, POSTA 2009 - Valencia, Spain
Duration: Sep 2 2009Sep 4 2009

Publication series

NameLecture Notes in Control and Information Sciences
Volume389
ISSN (Print)0170-8643

Other

Other3rd Multidisciplinary Symposium on Positive Systems: Theory and Applications, POSTA 2009
CountrySpain
CityValencia
Period9/2/099/4/09

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ASJC Scopus subject areas

  • Library and Information Sciences

Cite this

Salceanu, P. L., & Smith, H. (2009). Lyapunov exponents and uniform weak normally repelling invariant sets. In Positive Systems - Proceedings of the third Multidisciplinary International Symposium on Positive Systems: Theory and Applications, POSTA 2009 (pp. 17-27). (Lecture Notes in Control and Information Sciences; Vol. 389). https://doi.org/10.1007/978-3-642-02894-6_2