扩散的几何机制：先验不稳定哈密顿系统的严格验证
A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems
摘要：
本文考虑一个有代表性的先验不稳定的2+1/2自由度哈密顿系统，对它应用Delshams等人的论文中介绍的几何扩散机制，Mem.Amer.Math.Soc.2006，并在Delshams和Huguet，Nonlinearity 2009中推广，并为扩散轨道的存在提供了明确，具体和易于验证的条件。假设的简化使我们能够沿着证明明确地执行计算，这有助于以易于理解的方式呈现扩散的几何机制。特别地，我们充分描述了散射映射的构造和两类动力学在正常双曲不变流形上的组合
英文摘要：
In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem. Amer. Math. Soc. 2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold
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