In this paper we consider the following class of Lagrangian systems: Lϵ,μ(q,˙q,Q,˙Q,t)=˙Q22+˙q22+ϵ(1−cosq)+μf(q,˙q,Q,˙Q,t,μ) which has been studied by many authors in connection with Arnold's diffusion. Extending [2] prove, by variational means, that, for suitable perturbations including for example: f(q,˙q,Q,˙Q,t,μ)=(1−cosq)(cosQ+cost)+μp−1sin(q+Q)(p>2) if μ is small enough, exists a diffusion orbit of Lϵ,μ such that ˙Q(t) undergoes a variation of order 1 in a time td polinomial in μ, td≈1μ2.

Some remarks on a variational approach to Arnold diffusion / Berti, Massimiliano. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 2:3(1996), pp. 307-314. [10.3934/dcds.1996.2.307]

Some remarks on a variational approach to Arnold diffusion

Berti, Massimiliano
1996-01-01

Abstract

In this paper we consider the following class of Lagrangian systems: Lϵ,μ(q,˙q,Q,˙Q,t)=˙Q22+˙q22+ϵ(1−cosq)+μf(q,˙q,Q,˙Q,t,μ) which has been studied by many authors in connection with Arnold's diffusion. Extending [2] prove, by variational means, that, for suitable perturbations including for example: f(q,˙q,Q,˙Q,t,μ)=(1−cosq)(cosQ+cost)+μp−1sin(q+Q)(p>2) if μ is small enough, exists a diffusion orbit of Lϵ,μ such that ˙Q(t) undergoes a variation of order 1 in a time td polinomial in μ, td≈1μ2.
1996
2
3
307
314
http://www.aimsciences.org/article/doi/10.3934/dcds.1996.2.307
Berti, Massimiliano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/13072
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