Periodic orbits of continuous and discontinuous piecewise linear differential systems via first integrals

Jaume Llibre; Marco Antonio Teixeira

doi:10.1007/s40863-017-0064-x

Periodic orbits of continuous and discontinuous piecewise linear differential systems via first integrals

Jaume Llibre, Marco Antonio Teixeira

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

© 2017, Instituto de Matemática e Estatística da Universidade de São Paulo. Our main concern is to discuss the existence of periodic orbits for certain piecewise linear differential systems in Rn, where the discontinuity set is a hypersurface Σ. Using the fact that every linear differential system is always completely integrable, we illustrate for two piecewise linear differential systems, one in R3 and the other in R4, how to study analytically their periodic solutions.

Original language	English
Pages (from-to)	121-135
Journal	Sao Paulo Journal of Mathematical Sciences
Volume	12
Issue number	1
DOIs	https://doi.org/10.1007/s40863-017-0064-x
Publication status	Published - 1 Jun 2018

Keywords

Continuous piecewise linear differential systems
Discontinuous piecewise differential systems
First integrals
Periodic orbits
Periodic solutions

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abstract = "{\textcopyright} 2017, Instituto de Matem{\'a}tica e Estat{\'i}stica da Universidade de S{\~a}o Paulo. Our main concern is to discuss the existence of periodic orbits for certain piecewise linear differential systems in Rn, where the discontinuity set is a hypersurface Σ. Using the fact that every linear differential system is always completely integrable, we illustrate for two piecewise linear differential systems, one in R3 and the other in R4, how to study analytically their periodic solutions.",

keywords = "Continuous piecewise linear differential systems, Discontinuous piecewise differential systems, First integrals, Periodic orbits, Periodic solutions",

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AU - Teixeira, Marco Antonio

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N2 - © 2017, Instituto de Matemática e Estatística da Universidade de São Paulo. Our main concern is to discuss the existence of periodic orbits for certain piecewise linear differential systems in Rn, where the discontinuity set is a hypersurface Σ. Using the fact that every linear differential system is always completely integrable, we illustrate for two piecewise linear differential systems, one in R3 and the other in R4, how to study analytically their periodic solutions.

AB - © 2017, Instituto de Matemática e Estatística da Universidade de São Paulo. Our main concern is to discuss the existence of periodic orbits for certain piecewise linear differential systems in Rn, where the discontinuity set is a hypersurface Σ. Using the fact that every linear differential system is always completely integrable, we illustrate for two piecewise linear differential systems, one in R3 and the other in R4, how to study analytically their periodic solutions.

KW - Continuous piecewise linear differential systems

KW - Discontinuous piecewise differential systems

KW - First integrals

KW - Periodic orbits

KW - Periodic solutions

U2 - 10.1007/s40863-017-0064-x

DO - 10.1007/s40863-017-0064-x

M3 - Article

VL - 12

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EP - 135

JO - Sao Paulo Journal of Mathematical Sciences

JF - Sao Paulo Journal of Mathematical Sciences

SN - 1982-6907

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