Arnold Diffusion, Quantitative Estimates, and Stochastic Behavior in the <scp>Three‐Body</scp> Problem
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Publication:6049736
DOI10.1002/cpa.22014zbMath1529.37035arXiv1812.03665OpenAlexW3186557962MaRDI QIDQ6049736
Maciej J. Capiński, Marian Gidea
Publication date: 11 October 2023
Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1812.03665
Three-body problems (70F07) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Dynamical systems in classical and celestial mechanics (37N05)
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Topological shadowing methods in arnold diffusion: weak torsion and multiple time scales ⋮ A counterexample to the theorem of Laplace-Lagrange on the stability of semimajor axes ⋮ Arnold Diffusion in a Model of Dissipative System
Cites Work
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- Instability of high dimensional Hamiltonian systems: multiple resonances do not impede diffusion
- Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem
- 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
- Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action
- Speed of Arnold diffusion for analytic Hamiltonian systems
- A functional analysis approach to Arnold diffusion
- Arnold diffusion in Hamiltonian systems: a priori unstable case
- Analysis of the chaotic behaviour of orbits diffusing along the Arnold web
- Unbounded energy growth in Hamiltonian systems with a slowly varying parameter
- Resonance transport in near-integrable systems with many degrees of freedom
- Covering relations, cone conditions and the stable manifold theorem
- A numerical study of Arnold diffusion in a priori unstable systems
- Regular and chaotic dynamics.
- Frequency analysis for multi-dimensional systems. Global dynamics and diffusion
- Drift in phase space: A new variational mechanism with optimal diffusion time
- Fast Arnold diffusion in systems with three time scales
- A rigorous ODE solver and Smale's 14th problem
- Global instability in the restricted planar elliptic three body problem
- Arnold diffusion in perturbations of analytic integrable Hamiltonian systems
- \(C^1\) Lohner algorithm.
- Covering relations for multidimensional dynamical systems
- Transition tori in the five-body problem
- Transition map and shadowing lemma for normally hyperbolic invariant manifolds
- A geometric approach to the existence of orbits with unbounded energy in generic periodic perturbations by a potential of generic geodesic flows of \(\mathbb{T}^2\)
- CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems
- Semi-analytic computations of the speed of Arnold diffusion along single resonances in a priori stable Hamiltonian systems
- Arnold diffusion of charged particles in ABC magnetic fields
- Arnol'd diffusion in the elliptic restricted three-body problem
- First numerical evidence of global Arnold diffusion in quasi-integrable systems
- 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
- Diffusion times and stability exponents for nearly integrable analytic systems
- Topological methods in the instability problem of Hamiltonian systems
- Diffusion along transition chains of invariant tori and Aubry–Mather sets
- Verification methods: Rigorous results using floating-point arithmetic
- Arnold diffusion far from strong resonances in multidimensionala prioriunstable Hamiltonian systems
- Arnold diffusion in a restricted planar four-body problem
- Arnold diffusion in the planar elliptic restricted three-body problem: mechanism and numerical verification
- Transition tori in the planar restricted elliptic three-body problem
- An Example of Instability in High-dimensional Hamiltonian Systems
- A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model
- Diffusion speed in the Mather problem
- Unbounded growth of energy in nonautonomous Hamiltonian systems
- Evolution of slow variables ina prioriunstable Hamiltonian systems
- Trajectories in a neighbourhood of asymptotic surfaces ofa prioriunstable Hamiltonian systems
- An approach to arnold's diffusion through the calculus of variations
- A General Mechanism of Diffusion in Hamiltonian Systems: Qualitative Results
- Brownian Motion
- Upper bounds on Arnold diffusion time via Mather theory
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