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Reducing or enhancing chaos using periodic orbits

Romain Bachelard·Cristel Chandre·Xavier Leoncini
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Abstract

A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local bifurcations). Depending on the values of the residues, reflecting their linear stability properties, a set of invariant tori is destroyed or created in the neighborhood of the chosen periodic orbits. An application on a paradigmatic system, a forced pendulum, illustrates the method.

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Romain Bachelard, Cristel Chandre, Xavier Leoncini. 2006-01-19. Reducing or enhancing chaos using periodic orbits. https://doi.org/10.1063/1.2189157

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