Instability of high dimensional Hamiltonian systems: multiple resonances do not impede diffusion
From MaRDI portal
Publication:266143
DOI10.1016/j.aim.2015.11.010zbMath1355.37074arXiv1306.4614OpenAlexW1884565747MaRDI QIDQ266143
Amadeu Delshams, Rafael de la Llave, Teresa M. Seara
Publication date: 13 April 2016
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1306.4614
Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25)
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Cites Work
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- Arnold diffusion. I: Announcement of results
- Speed of Arnold diffusion for analytic Hamiltonian systems
- A functional analysis approach to Arnold diffusion
- Unbounded energy growth in Hamiltonian systems with a slowly varying parameter
- Resonance transport in near-integrable systems with many degrees of freedom
- Coupled oscillator models with no scale separation
- Estimates in the Kolmogorov theorem on conservation of conditionally periodic motions
- Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation
- Multiphase averaging for classical systems. With applications to adiabatic theorems. Transl. from the French by H. S. Dumas
- Moser's implicit function theorem in the framework of analytic smoothing
- Universal homoclinic bifurcations and chaos near double resonances
- Arnold's diffusion with two resonances
- Drift in phase space: A new variational mechanism with optimal diffusion time
- Multidimensional symplectic separatrix maps
- Chaos near resonance
- Hamiltonian systems with orbits covering densely submanifolds of small codimension
- Lectures on partial hyperbolicity and stable ergodicity
- Transition tori in the five-body problem
- A geometric approach to the existence of orbits with unbounded energy in generic periodic perturbations by a potential of generic geodesic flows of \(\mathbb{T}^2\)
- Geometric properties of the scattering map of a normally hyperbolic invariant manifold
- Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows.
- Existence of diffusion orbits in a priori unstable Hamiltonian systems
- Topological methods in the instability problem of Hamiltonian systems
- A lecture on the classical KAM theorem
- Arnold diffusion far from strong resonances in multidimensionala prioriunstable Hamiltonian systems
- Arnold diffusion in a restricted planar four-body problem
- Transition tori in the planar restricted elliptic three-body problem
- Arnold's Diffusion: from the a priori unstable to the a priori stable case
- Introduction to the Perturbation Theory of Hamiltonian Systems
- Integrability of hamiltonian systems on cantor sets
- A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model
- Geography of resonances and Arnold diffusion ina prioriunstable Hamiltonian systems
- Diffusion speed in the Mather problem
- Separatrix maps in Hamiltonian systems
- Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems
- Generalized implicit function theorems with applications to some small divisor problems, I
- Generalized implicit function theorems with applications to some small divisor problems, II
- Unbounded growth of energy in nonautonomous Hamiltonian systems
- Differentiable invariant manifolds for partially hyperbolic tori and a lambda lemma
- Evolution of slow variables ina prioriunstable Hamiltonian systems
- A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: Announcement of results
- PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
- Invariant manifolds
- Upper bounds on Arnold diffusion time via Mather theory
