Isochronicity for several classes of Hamiltonian systems

A. Cima, F. Mañosas, J. Villadelprat

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67 Citations (Scopus)

Abstract

In this paper we study isochronous centers of analytic Hamiltonian systems giving special attention to the polynomial case. We first revisit the potential systems and we show the connection between isochronicity and involutions. We then study a more general system, namely the ones associated to Hamiltonians of the form H(x, y)=A(x)+B(x)y+C(x)y2. As an application we classify the cubic polynomial Hamiltonian isochronous centers and we give examples of nontrivial and nonglobal polynomial Hamiltonian isochronous centers. © 1999 Academic Press.
Original languageEnglish
Pages (from-to)373-413
JournalJournal of Differential Equations
Volume157
Issue number2
DOIs
Publication statusPublished - 20 Sep 1999

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