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A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems.
- Source :
- Communications in Mathematical Physics; Nov2016, Vol. 348 Issue 1, p321-361, 41p
- Publication Year :
- 2016
-
Abstract
- In this paper we study a so-called separatrix map introduced by Zaslavskii-Filonenko (Sov Phys JETP 27:851-857, 1968) and studied by Treschev (Physica D 116(1-2):21-43, 1998; J Nonlinear Sci 12(1):27-58, 2002), Piftankin (Nonlinearity (19):2617-2644, 2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3-108, 2007). We derive a second order expansion of this map for trigonometric perturbations. In Castejon et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint available at , 2015), Guardia and Kaloshin (Stochastic diffusive behavior through big gaps in a priori unstable systems (in preparation), 2015), and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior for the generalized Arnold example away from resonances. Preprint available at , 2015), applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00103616
- Volume :
- 348
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Communications in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 118355073
- Full Text :
- https://doi.org/10.1007/s00220-016-2705-9