Limit cycles of piecewise smooth differential equations on two dimensional torus
type: Item
instance of: scholarly article
title: Limit cycles of piecewise smooth differential equations on two dimensional torus
zbMATH Open document ID: 1410.34095
author: Jaume Llibre
author: Ricardo Miranda Martins
author: Durval J. Tonon
published in: Journal of Dynamics and Differential Equations
publication date: 2018-11-06T00:00:00Z
full work available at URL: http://ddd.uab.cat/record/221390
review text: In this paper, the authors study the limit cycles of some classes of piecewise smooth vector fields defined on the two dimensional torus. Considering these vector fields, the authors characterize the global dynamics by studying the upper bound of number of limit cycles, the existence of non-trivial recurrence and a continuum of periodic orbits and also present a family of piecewise smooth vector fields that posses a finite number of fold points proving that for any \(2k\) number of limit cycles there exists a piecewise smooth vector field in this family that presents \(k\) limit cycles.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C40
zbMATH DE Number: 6973925
zbMATH Keywords: piecewise smooth differential equations
zbMATH Keywords: global dynamics on torus
zbMATH Keywords: limit cycles
reviewed by: Valery A. Gaiko
MaRDI profile type: Publication
OpenAlex ID: W2602635786
cites work: Dynamics of non-ergodic piecewise affine maps of the torus.
cites work: ON PLANAR PIECEWISE AND TWO-TORUS PARABOLIC MAPS
cites work: Q5733898
cites work: Ergodic and statistical properties of piecewise linear hyperbolic automorphisms of the 2-torus
cites work: Piecewise-smooth dynamical systems. Theory and applications
cites work: Q3994508
cites work: Q5534404
cites work: On extended Chebyshev systems with positive accuracy
cites work: Discontinuous systems. Lyapunov analysis and robust synthesis under uncertainty conditions
DOI: 10.1007/S10884-017-9584-4
description: scientific article; zbMATH DE number 6973925