Arnold diffusion for an a priori unstable Hamiltonian system with 3 $+$ 1/2 degrees of freedom
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913357076889600 |
|---|---|
| author | Delshams, Amadeu Granados, Albert Schaefer, Rodrigo G. |
| author_facet | Delshams, Amadeu Granados, Albert Schaefer, Rodrigo G. |
| contents | In the present paper we apply the geometrical mechanism of diffusion in an \emph{a priori} unstable Hamiltonian system with 3 $+$ 1/2 degrees of freedom. This mechanism consists of combining iterations of the \emph{inner} and \emph{outer} dynamics associated to a \emph{Normallly Hyperbolic Invariant Manifold} (NHIM), to construct diffusing \emph{pseudo-orbits} and subsequently apply shadowing results to prove the existence of diffusing orbits of the system.
In addition to proving the existence of diffusion for a wide range of the parameters of the system, an important part of our study focuses on the search for \emph{Highways}, a particular family of orbits of the outer map (the so-called \emph{scattering} map), whose existence is sufficient to ensure a very large drift of the action variables, with a diffusion time near them that agrees with the optimal estimates in the literature. Moreover, this optimal diffusion time is calculated, with an explicit calculation of the constants involved. All these properties are proved by analytical methods and, where necessary, supplemented by numerical calculations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18787 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Arnold diffusion for an a priori unstable Hamiltonian system with 3 $+$ 1/2 degrees of freedom Delshams, Amadeu Granados, Albert Schaefer, Rodrigo G. Dynamical Systems 37J40 In the present paper we apply the geometrical mechanism of diffusion in an \emph{a priori} unstable Hamiltonian system with 3 $+$ 1/2 degrees of freedom. This mechanism consists of combining iterations of the \emph{inner} and \emph{outer} dynamics associated to a \emph{Normallly Hyperbolic Invariant Manifold} (NHIM), to construct diffusing \emph{pseudo-orbits} and subsequently apply shadowing results to prove the existence of diffusing orbits of the system. In addition to proving the existence of diffusion for a wide range of the parameters of the system, an important part of our study focuses on the search for \emph{Highways}, a particular family of orbits of the outer map (the so-called \emph{scattering} map), whose existence is sufficient to ensure a very large drift of the action variables, with a diffusion time near them that agrees with the optimal estimates in the literature. Moreover, this optimal diffusion time is calculated, with an explicit calculation of the constants involved. All these properties are proved by analytical methods and, where necessary, supplemented by numerical calculations. |
| title | Arnold diffusion for an a priori unstable Hamiltonian system with 3 $+$ 1/2 degrees of freedom |
| topic | Dynamical Systems 37J40 |
| url | https://arxiv.org/abs/2310.18787 |