Non-isochronicity on piecewise Hamiltonian differential systems with homogeneous nonlinearities

Abstract

In this paper, we prove the non-isochronicity of Σ-centres 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 centre and only homogeneous nonlinearities. This result generalizes a classical result of non-isochronicity on the smooth Hamiltonian systems with homogeneous nonlinearities.

Keywords:

• Piecewise differential systems
• Hamiltonian differential systems
• isochronous centre
• period function

2020 MSC:

• 34A36
• 34C25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the China Scholarship Council under Grant No. 202306780018.