TY - GEN

T1 - Lyapunov exponents and uniform weak normally repelling invariant sets

AU - Salceanu, Paul Leonard

AU - Smith, Hal

PY - 2009/12/1

Y1 - 2009/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77953959614&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-02894-6_2

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

M3 - Conference contribution

AN - SCOPUS:77953959614

SN - 9783642028939

T3 - Lecture Notes in Control and Information Sciences

SP - 17

EP - 27

BT - Positive Systems - Proceedings of the third Multidisciplinary International Symposium on Positive Systems

T2 - 3rd Multidisciplinary Symposium on Positive Systems: Theory and Applications, POSTA 2009

Y2 - 2 September 2009 through 4 September 2009

ER -