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Non-isochronicity on piecewise Hamiltonian differential systems with homogeneous nonlinearities

Xiaoyi Chen, Guangfeng Dong

Abstract

In this paper we prove the non-isochronicity of $Σ$-centers for a class of planar piecewise smooth differential systems with a straight switching line, whose two sub-systems are Hamiltonian differential systems with a non-degenerated center and only homogeneous nonlinearities.

Non-isochronicity on piecewise Hamiltonian differential systems with homogeneous nonlinearities

Abstract

In this paper we prove the non-isochronicity of -centers for a class of planar piecewise smooth differential systems with a straight switching line, whose two sub-systems are Hamiltonian differential systems with a non-degenerated center and only homogeneous nonlinearities.
Paper Structure (3 sections, 8 theorems, 37 equations)

This paper contains 3 sections, 8 theorems, 37 equations.

Table of Contents

  1. Introduction and the main results
  2. Preliminaries
  3. Proof of the main results

Key Result

Theorem 1

For system $X$ the origin is not an isochronous $\Sigma$-center for any $n\geq 1$ and $m\geq 1$.

Theorems & Definitions (14)

  • Theorem 1
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • Proposition 5: Theorems A and C in Gasull
  • Lemma 6
  • proof
  • proof : Proof of Proposition \ref{['pro-1']}
  • Lemma 7
  • proof
  • ...and 4 more