A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems

Abstract

In this paper we study a so-called separatrix map introduced by Zaslaskii-Filonenko [ZF68] and studied by Treschev and Piftankin [Tre98, Tre02, Pif06, PT07]. We derive a second order expansion of this map for trigonometric perturbations. In [CK15, GK15], and [KZZ15], applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior.

References in corpus (2)

• Normally Hyperbolic Invariant Laminations and diffusive behaviour for the generalized Arnold example away from resonances
• Orbits of nearly integrable systems accumulating to KAM tori

Cited by in corpus (4)

• Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems
• Random Iteration of Cylinder Maps and diffusive behavior away from resonances
• Gevrey genericity of Arnold diffusion in a priori unstable Hamiltonian systems
• Arnold diffusion in multidimensional a priori unstable Hamiltonian systems