Two-dimensional isochronous nonstandard Hamiltonian systems

Abstract

Abstract. We identify a generic class of two dimensional nonstandard Hamiltonian systems which exhibit isochronous behaviour. This class of systems belongs to the two dimensional mixed Liénard-type equations and is obtained by generalizing the scalar modified Emden equation (MEE) to two dimensions. We show that the generalized class of equations admits a Hamiltonian description and exhibits periodic and quasiperiodic oscillations for suitable choice of parameters and also PT symmetric property.

Isochronous Liénard-type nonlinear oscillators of arbitrary dimensions

“…We also note here that one can make appropriate contact-type transformations to (47) which maps them onto a system of N uncoupled harmonic oscillators.…”

“…Due to its importance, this property can be used to identify such Hamiltonian systems by a suitable generalization of the P T -symmetric Lagrangian. For this purpose, one can define the nonstandard Lagrangian as [47] …”