Existence of poincaré maps in piecewise linear differential systems in ℝN

Jaume Llibre; Antonio E. Teruel

doi:https://doi.org/10.1142/S0218127404010874

Existence of poincaré maps in piecewise linear differential systems in ℝ^N

Jaume Llibre, Antonio E. Teruel

Department of Mathematics

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

19 Citations (Scopus)

Abstract

In this paper we present a relationship between the algebraic notion of proper system, the geometric notion of contact point and the dynamic notion of Poincaré map for piecewise linear differential systems. This allows to present sufficient conditions (which are also necessary under additional hypotheses) for the existence of Poincaré maps in piecewise linear differential systems. Moreover, an adequate parametrization of the Poincaré maps make such maps invariant under linear transformations.

Original language	English
Pages (from-to)	2843-2851
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	14
DOIs	https://doi.org/10.1142/S0218127404010874
Publication status	Published - 1 Jan 2004

Keywords

Piecewise linear differential systems
Poincaré map

Access to Document

https://doi.org/10.1142/S0218127404010874

Cite this

@article{43fa1074b3f743569a1501e2ece2e978,

title = "Existence of poincar{\'e} maps in piecewise linear differential systems in ℝN",

abstract = "In this paper we present a relationship between the algebraic notion of proper system, the geometric notion of contact point and the dynamic notion of Poincar{\'e} map for piecewise linear differential systems. This allows to present sufficient conditions (which are also necessary under additional hypotheses) for the existence of Poincar{\'e} maps in piecewise linear differential systems. Moreover, an adequate parametrization of the Poincar{\'e} maps make such maps invariant under linear transformations.",

keywords = "Piecewise linear differential systems, Poincar{\'e} map",

author = "Jaume Llibre and Teruel, {Antonio E.}",

year = "2004",

month = jan,

day = "1",

doi = "https://doi.org/10.1142/S0218127404010874",

language = "English",

volume = "14",

pages = "2843--2851",

}

TY - JOUR

T1 - Existence of poincaré maps in piecewise linear differential systems in ℝN

AU - Llibre, Jaume

AU - Teruel, Antonio E.

PY - 2004/1/1

Y1 - 2004/1/1

N2 - In this paper we present a relationship between the algebraic notion of proper system, the geometric notion of contact point and the dynamic notion of Poincaré map for piecewise linear differential systems. This allows to present sufficient conditions (which are also necessary under additional hypotheses) for the existence of Poincaré maps in piecewise linear differential systems. Moreover, an adequate parametrization of the Poincaré maps make such maps invariant under linear transformations.

AB - In this paper we present a relationship between the algebraic notion of proper system, the geometric notion of contact point and the dynamic notion of Poincaré map for piecewise linear differential systems. This allows to present sufficient conditions (which are also necessary under additional hypotheses) for the existence of Poincaré maps in piecewise linear differential systems. Moreover, an adequate parametrization of the Poincaré maps make such maps invariant under linear transformations.

KW - Piecewise linear differential systems

KW - Poincaré map

U2 - https://doi.org/10.1142/S0218127404010874

DO - https://doi.org/10.1142/S0218127404010874

M3 - Article

SN - 0218-1274

VL - 14

SP - 2843

EP - 2851

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering