Gevrey genericity of Arnold diffusion in a priori unstable Hamiltonian systems
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Publication:5147950
DOI10.1088/1361-6544/abb44fzbMath1459.37049arXiv1710.07942OpenAlexW3122879870MaRDI QIDQ5147950
Publication date: 29 January 2021
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1710.07942
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) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09)
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Cites Work
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- Instability of high dimensional Hamiltonian systems: multiple resonances do not impede diffusion
- A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems
- Normal forms, stability and splitting of invariant manifolds. I: Gevrey Hamiltonians
- Destruction of invariant circles for Gevrey area-preserving twist map
- Regular dependence of the Peierls barriers on perturbations
- Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders
- Arnold diffusion. I: Announcement of results
- Large normally hyperbolic cylinders in a priori stable Hamiltonian systems
- A geometric mechanism of diffusion: rigorous verification in a priori unstable Hamiltonian systems
- Effective stability for Gevrey and finitely differentiable prevalent Hamiltonians
- Speed of Arnold diffusion for analytic Hamiltonian systems
- A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems
- A functional analysis approach to Arnold diffusion
- Global normally hyperbolic invariant cylinders in Lagrangian systems
- Arnold diffusion in Hamiltonian systems: a priori unstable case
- Action minimizing invariant measures for positive definite Lagrangian systems
- Unbounded energy growth in Hamiltonian systems with a slowly varying parameter
- On the Conley decomposition of Mather sets
- The implicit function theorem for ultradifferentiable mappings
- Variational construction of connecting orbits
- Drift in phase space: A new variational mechanism with optimal diffusion time
- Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems
- The Palais-Smale condition and Mañé's critical values
- Multidimensional symplectic separatrix maps
- Connecting orbits of time dependent Lagrangian systems
- Arnold diffusion in perturbations of analytic integrable Hamiltonian systems
- Symbolic dynamics and Arnold diffusion
- Lectures on partial hyperbolicity and stable ergodicity
- A geometric approach to the existence of orbits with unbounded energy in generic periodic perturbations by a potential of generic geodesic flows of \(\mathbb{T}^2\)
- KAM tori are no more than sticky
- The genericity of Arnold diffusion in nearly integrable Hamiltonian systems
- Uniform hyperbolicity of invariant cylinder
- Arnold diffusion in a priori chaotic symplectic maps
- A generic property of families of Lagrangian systems
- Dynamics around the double resonance
- Geometric properties of the scattering map of a normally hyperbolic invariant manifold
- Existence of diffusion orbits in a priori unstable Hamiltonian systems
- Diffusion times and stability exponents for nearly integrable analytic systems
- On diffusion in high-dimensional Hamiltonian systems
- Arnold diffusion far from strong resonances in multidimensionala prioriunstable Hamiltonian systems
- Improved exponential stability for near-integrable quasi-convex Hamiltonians
- Arnold diffusion for smooth convex systems of two and a half degrees of freedom
- KAM, α-Gevrey regularity and the α-Bruno-Rüssmann condition
- 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
- Geometry of Arnold Diffusion
- The dynamics of pseudographs in convex Hamiltonian systems
- Unbounded growth of energy in nonautonomous Hamiltonian systems
- Generic properties and problems of minimizing measures of Lagrangian systems
- Evolution of slow variables ina prioriunstable Hamiltonian systems
- A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: Announcement of results
- An approach to arnold's diffusion through the calculus of variations
- A General Mechanism of Diffusion in Hamiltonian Systems: Qualitative Results
- Arnold Diffusion by Variational Methods
- Wandering domains and random walks in Gevrey near-integrable systems
- KAM theorem for Gevrey Hamiltonians
- Shadowing orbits for transition chains of invariant tori alternating with Birkhoff zones of instability
- Measure and Capacity of Wandering Domains in Gevrey Near-integrable Exact Symplectic Systems
- Connecting orbits of autonomous Lagrangian systems
- Invariant manifolds
- Upper bounds on Arnold diffusion time via Mather theory
