先验不稳定系统三角扰动分界线映射的二阶展开
A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems
摘要：
本文研究了由Zaslaskii-Filonenko [ZF 68]引入并由Treschev和Piftankin [Tre 98，Tre 02，Pif 06，PT 07]研究的所谓分界线映射.我们推导出这个映射的三角摄动的二阶展开。在[CK 15，GK 15]和[KZZ 15]中，应用本文的结果，我们描述了一类具有随机扩散行为的近可积确定性系统。
英文摘要：
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.
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