TL;DR
This paper provides a comprehensive set of explicit conditions, expressed via Taylor coefficients, that determine when a one-degree-of-freedom Hamiltonian system exhibits isochronicity, meaning equal period for all oscillations.
Contribution
It offers the first complete characterization of isochronicity conditions for 1 DOF Hamiltonian systems in terms of Taylor coefficients.
Findings
Derived explicit necessary and sufficient conditions for isochronicity.
Presented conditions in terms of Taylor coefficients of the Hamiltonian.
Complete characterization of isochronicity for 1 DOF systems.
Abstract
Our main result is the complete set of explicit conditions necessary and sufficient for isochronicity of a Hamiltonian system with one degree of freedom. The conditions are presented in terms of Taylor coefficients of the Hamiltonian function.
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