Abstract
Two algorithms are given for finding conditions for a critical point to be an isochronous center. The first is based on a systematic search for a transformation to the simple harmonic oscillator and as an example is used to find conditions for an isochronous center in the Kukles system; the second algorithm is specific to systems with homogeneous nonlinearities and is based on a connection with an Abel differential equation. General properties of systems with isochronous centers are also considered and results on Lienard and Hamiltonian systems are deduced; a close connection is demonstrated between isochronous centers and complex centers.
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