\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Fixed point theorems in the Arnol'd model about instability of the action-variables in phase-space

Abstract Related Papers Cited by
  • We consider the hamiltonian $H=1/2(I_1^2+I_2^2)+\varepsilon(\cos\varphi_1-1) (1+\mu(\sin\varphi_2+\cos t))$ $I\in\mathbb{R}^2$ ("Arnol'd model about diffusion"); by means of fixed point theorems, the existence of the stable and unstable manifolds (whiskers) of invariant, "a priori unstable tori", for any vector-frequency $(\omega,1)\in\mathbb{R}^2$ is proven. Our aim is to provide detailed proofs which are missing in Arnol'd's paper, namely prove the content of the Assertion B pag.583 of [A]. Our proofs are based on technical tools suggested by Arnol'd i.e. the contraction mapping method together with the "conical metric" (see the footnote ** of pag. 583 of [A]).
    Mathematics Subject Classification: 37C25.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(74) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return