Lyapunov exponents and uniform weak normally repelling invariant sets

Paul Leonard Salceanu; Hal Smith

doi:10.1007/978-3-642-02894-6_2

Lyapunov exponents and uniform weak normally repelling invariant sets

Paul Leonard Salceanu, Hal Smith

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Positive Systems - Proceedings of the third Multidisciplinary International Symposium on Positive Systems
Subtitle of host publication	Theory and Applications, POSTA 2009
Pages	17-27
Number of pages	11
DOIs	https://doi.org/10.1007/978-3-642-02894-6_2
State	Published - 2009
Event	3rd Multidisciplinary Symposium on Positive Systems: Theory and Applications, POSTA 2009 - Valencia, Spain Duration: Sep 2 2009 → Sep 4 2009

Publication series

Name	Lecture Notes in Control and Information Sciences
Volume	389
ISSN (Print)	0170-8643

Other

Other	3rd Multidisciplinary Symposium on Positive Systems: Theory and Applications, POSTA 2009
Country/Territory	Spain
City	Valencia
Period	9/2/09 → 9/4/09

ASJC Scopus subject areas

Library and Information Sciences

Access to Document

10.1007/978-3-642-02894-6_2

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

Lyapunov exponents and uniform weak normally repelling invariant sets. / Salceanu, Paul Leonard; Smith, Hal.
Positive Systems - Proceedings of the third Multidisciplinary International Symposium on Positive Systems: Theory and Applications, POSTA 2009. 2009. p. 17-27 (Lecture Notes in Control and Information Sciences; Vol. 389).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Salceanu, PL & 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. Lecture Notes in Control and Information Sciences, vol. 389, pp. 17-27, 3rd Multidisciplinary Symposium on Positive Systems: Theory and Applications, POSTA 2009, Valencia, Spain, 9/2/09. https://doi.org/10.1007/978-3-642-02894-6_2

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Lyapunov exponents and uniform weak normally repelling invariant sets

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