Isochronicity for a class of reversible systems

This paper deals with the relation between isochronicity and first integral for a class of reversible systems: (x) over dot = -U(x)y, (y) over dot = f(x, y). which associates to the first integral of the form H(x, y) = F(x)y(2) + G(x). Two necessary and sufficient conditions are given to characterize isochronicity for these systems. Moreover. we apply these results to show that there exists a class of polynomial reversible systems of degree n with isochronous center for any n. (C) 2009 Elsevier Inc. All rights reserved.