Arnold's Diffusion: From the a priori Unstable to the a priori Stable Case

被引：0

作者：

Bernard, Patrick ^{[1
]}

机构：

[1] CEREMADE, CNRS, UMR 7534, Pl Marechal Lattre Tassigny, F-75775 Paris, France

来源：

PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS, VOL III: INVITED LECTURES | 2010年

关键词：

Arnold's diffusion; normally hyperbolic cylinder; partially hyperbolic tori; homoclinic intersections; Weak KAM solutions; variational methods; action minimization; PARTIALLY HYPERBOLIC TORI; INTEGRABLE HAMILTONIAN-SYSTEMS; CONNECTING ORBITS; INVARIANT TORI; LAMBDA-LEMMA; PERIODIC PERTURBATIONS; LAGRANGIAN SYSTEMS; HOMOCLINIC ORBITS; UNBOUNDED ENERGY; GEODESIC-FLOWS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We expose some selected topics concerning the instability of the action variables in a priori unstable Hamiltonian systems, and outline a new strategy that may allow to apply these methods to a priori stable systems.

引用

页码：1680 / 1700

页数：21

共 10 条

[1] ARNOLD DIFFUSION IN HAMILTONIAN SYSTEMS: A PRIORI UNSTABLE CASE
Cheng, Chong-Qing
Yan, Jun
JOURNAL OF DIFFERENTIAL GEOMETRY, 2009, 82 (02) : 229 - 277
[2] Gevrey genericity of Arnold diffusion in a priori unstable Hamiltonian systems
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NONLINEARITY, 2021, 34 (01) : 455 - 508
[3] Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems
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NONLINEARITY, 2009, 22 (08) : 1997 - 2077
[4] Arnold Diffusion in A Priori Chaotic Symplectic Maps
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COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2017, 353 (02) : 507 - 547
[5] Arnold diffusion far from strong resonances in multidimensional a priori unstable Hamiltonian systems
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NONLINEARITY, 2012, 25 (09) : 2717 - 2757
[6] Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems
Chen, Qinbo
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NONLINEARITY, 2022, 35 (04) : 1986 - 2019
[7] Large Normally Hyperbolic Cylinders in a priori Stable Hamiltonian Systems
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ANNALES HENRI POINCARE, 2010, 11 (05): : 929 - 942
[8] A Second Order Expansion of the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems
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Zhang, J.
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2016, 348 (01) : 321 - 361
[9] An approach to Arnold's diffusion through the calculus of variations
Bessi, U
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1996, 26 (06) : 1115 - 1135
[10] Arnold's mechanism of diffusion in the spatial circular restricted three-body problem: A semi-analytical argument
Delshams, Amadeu
Gidea, Marian
Roldan, Pablo
PHYSICA D-NONLINEAR PHENOMENA, 2016, 334 : 29 - 48

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