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

Guardia M, Kaloshin V, Zhang J. 2016. A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. Communications in Mathematical Physics. 348, 321–361.

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Journal Article | Published | English
Author
Guardia, M.; Kaloshin, VadimIST Austria ; Zhang, J.
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 arXiv:1501.03319, 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 http://www.terpconnect.umd.edu/vkaloshi/, 2015), applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior.
Publishing Year
Date Published
2016-11-01
Journal Title
Communications in Mathematical Physics
Volume
348
Page
321-361
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Guardia M, Kaloshin V, Zhang J. A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. Communications in Mathematical Physics. 2016;348:321-361. doi:10.1007/s00220-016-2705-9
Guardia, M., Kaloshin, V., & Zhang, J. (2016). A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-016-2705-9
Guardia, M., Vadim Kaloshin, and J. Zhang. “A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems.” Communications in Mathematical Physics. Springer Nature, 2016. https://doi.org/10.1007/s00220-016-2705-9.
M. Guardia, V. Kaloshin, and J. Zhang, “A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems,” Communications in Mathematical Physics, vol. 348. Springer Nature, pp. 321–361, 2016.
Guardia M, Kaloshin V, Zhang J. 2016. A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems. Communications in Mathematical Physics. 348, 321–361.
Guardia, M., et al. “A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems.” Communications in Mathematical Physics, vol. 348, Springer Nature, 2016, pp. 321–61, doi:10.1007/s00220-016-2705-9.

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