On periodic orbits of polynomial relay systems

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April 2007, 17(2): 331-347. doi: 10.3934/dcds.2007.17.331

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, France
2.	Instituto de Matemática e Estatística, University of Campinas, Campinas, Brazil

Received December 2005 Revised September 2006 Published November 2006

Abstract
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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.

Keywords: semi-algebraic sets., discontinuous differential equations, periodic orbits.

Mathematics Subject Classification: 34A36, 37-04, 37G1.

Citation: Alain Jacquemard, Weber Flávio Pereira. On periodic orbits of polynomial relay systems. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 331-347. doi: 10.3934/dcds.2007.17.331

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