On periodic orbits of polynomial relay systems

Alain Jacquemard; Weber Flávio Pereira

doi:10.3934/dcds.2007.17.331

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2007, Volume 17, Issue 2: 331-347. Doi: 10.3934/dcds.2007.17.331

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On periodic orbits of polynomial relay systems

Alain Jacquemard^1, and
Weber Flávio Pereira^2,

1.
Institut de Mathématiques de Bourgogne, UMR CNRS 5584, Université de Bourgogne, Dijon
2.
Instituto de Matemática e Estatística, University of Campinas, Campinas

Received: November 30, 2005

Revised: August 31, 2006

Published: April 2007

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Abstract

We present an algorithm which determines global conditions for a class of discontinuous vector fields in 4D (called polynomial relay systems) to have periodic orbits. We present explicit results relying on constructive proofs, which involve classical Effective Algebraic Geometry algorithms.

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Mathematics Subject Classification: 34A36, 37-04, 37G15.

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