Arnold Diffusion in a Model of Dissipative System
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Publication:6132789
DOI10.1137/22m1525508zbMath1526.37077arXiv2206.14878MaRDI QIDQ6132789
Marian Gidea, Unnamed Author, Teresa M. Seara
Publication date: 17 August 2023
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2206.14878
Hamiltonian systemsArnold diffusionscattering mapdissipative perturbationsconformally symplectic system
Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Nearly integrable Hamiltonian systems, KAM theory (70H08) Dynamical aspects of twist maps (37E40) Symplectic and canonical mappings (37J11)
Cites Work
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- Local behavior near quasi-periodic solutions of conformally symplectic systems
- Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders
- Perturbations of geodesic flows by recurrent dynamics
- Arnold diffusion. I: Announcement of results
- A functional analysis approach to Arnold diffusion
- Some properties of locally conformal symplectic structures
- Arnold diffusion in Hamiltonian systems: a priori unstable case
- Unbounded energy growth in Hamiltonian systems with a slowly varying parameter
- Covering relations, cone conditions and the stable manifold theorem
- Quasi-periodic attractors in celestial mechanics
- Drift in phase space: A new variational mechanism with optimal diffusion time
- Global Melnikov theory in Hamiltonian systems with general time-dependent perturbations
- Invariant manifolds and the parameterization method in coupled energy harvesting piezoelectric oscillators
- Arnold diffusion for a complete family of perturbations
- Splitting potential and the Poincaré-Melnikov method for whiskered tori in Hamiltonian systems
- A geometric approach to the existence of orbits with unbounded energy in generic periodic perturbations by a potential of generic geodesic flows of \(\mathbb{T}^2\)
- Variational approach to Arnold diffusion
- Melnikov method for non-conservative perturbations of the restricted three-body problem
- Diffusing orbits along chains of cylinders
- Global effect of non-conservative perturbations on homoclinic orbits
- Arnold diffusion in a priori chaotic symplectic maps
- Viscoelastic tides: models for use in Celestial Mechanics
- A KAM theory for conformally symplectic systems: efficient algorithms and their validation
- Geometric properties of the scattering map of a normally hyperbolic invariant manifold
- Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows.
- Diffusion along transition chains of invariant tori and Aubry–Mather sets
- Arnold diffusion far from strong resonances in multidimensionala prioriunstable Hamiltonian systems
- Arnold diffusion for smooth convex systems of two and a half degrees of freedom
- 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
- Weakly Dissipative Systems in Celestial Mechanics
- A magnetoelastic strange attractor
- Unbounded growth of energy in nonautonomous Hamiltonian systems
- Evolution of slow variables ina prioriunstable Hamiltonian systems
- An analytical solution to the equation of motion for the damped nonlinear pendulum
- Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom
- A General Mechanism of Diffusion in Hamiltonian Systems: Qualitative Results
- Arnold Diffusion by Variational Methods
- Invariant manifolds
- Arnold Diffusion, Quantitative Estimates, and Stochastic Behavior in the <scp>Three‐Body</scp> Problem
- Arnold diffusion for a complete family of perturbations with two independent harmonics