Universal chaotic layer width in space-periodic Hamiltonian systems under adiabatic ac time-periodic forces

¹  Departamento de Física Aplicada, Escuela de Ingenierías Industriales, Universidad de Extremadura Apartado Postal 382, E-06071 Badajoz, Spain, EU
²  Laboratory of Nonlinear Dynamical Systems, V. I. Il'ichev Pacific Oceanological Institute of the Russian Academy of Sciences - 690041 Vladivostok, Russia

Corresponding author: rchacon@unex.es

Received: 5 February 2010
Accepted: 12 May 2010

Abstract

We study the dependence of the chaotic layer width in spatially periodic non-autonomous Hamiltonian systems on the waveform of adiabatic ac time-periodic forces. Contrary to common wisdom, we demonstrate through the universal model of a driven pendulum that both the chaotic layer width and the generalized adiabatic condition depend on the maximal impulse transmitted by the force over a period between two of its consecutive zeros —rather than on the force period— irrespective of its waveform. The theory is confirmed by extensive numerical experiments, and diverse applications including chaotic transport are discussed.