Work

Period Function for a Family of Piecewise Planar Hamiltonian Systems

Year: 2024

Type: article

Abstract: In this paper, we analyze the monotonicity and the number of critical periods of the period function associated with a family of piecewise planar continuous potential systems. In particular, we describe the bifurcation diagram of the period function, determining the regions of the parameter space where it is monotonically increasing or decreasing and where it has at most one simple critical period. In order to prove the main result, we rewrite such a function in terms of the two period functions of the uncoupled planar Hamiltonian systems matched by the separation line.

Source: International Journal of Bifurcation and Chaos

DOI: 10.1142/s0218127424501992

Authors: Alex C. Rezende, Mirianne A. S. Santos, Joan Torregrosa

Institutions: Universidade Federal de São Carlos, Universitat Autònoma de Barcelona, Centre de Recerca Matemàtica

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Ministerio de Ciencia, Innovación y Universidades, Fundação de Amparo à Pesquisa do Estado de São Paulo, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Agencia Estatal de Investigación

Awards: New frontiers in Singularity Theory, G7958417560, G84477964