Perturbation theory analysis of chaos

T. Shimizu

Physica A: Statistical Mechanics and its Applications, 1987, vol. 145, issue 3, 341-360

Abstract: The theory developed in a previous paper (I) is applied to a time-dependent Hamiltonian system, which is governed by a three-dimensional differential system. The transition from quasiperiodicity to chaos is discussed theoretically by using the nonlinear scale method. The transition is compared with that in a dissipative system. The time evolution of the system is decomposed into a fastly varying part and a slowly varying part. The slowly varying part is shown to vacillate for some initial conditions. The vacillation is deterministic, but depends sensitively on the initial conditions. The theoretical result is shown to be in a good agreement with that of the numerical simulation.

Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:145:y:1987:i:3:p:341-360

DOI: 10.1016/0378-4371(87)90001-X

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