Kirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problem
From MaRDI portal
Publication:344464
DOI10.4171/JEMS/642zbMath1404.70028arXiv1109.2892OpenAlexW2964276436MaRDI QIDQ344464
Pablo Roldán, Jacques Féjoz, Marcel Guardia, Vadim Yu. Kaloshin
Publication date: 22 November 2016
Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1109.2892
instabilitythree-body problemsolar systemArnold diffusionresonancehyperbolicityasteroid beltKirkwood gapMather mechanism
Three-body problems (70F07) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Celestial mechanics (70F15)
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Cites Work
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- Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action
- A functional analysis approach to Arnold diffusion
- Computing the scattering map in the spatial Hill's problem
- High-precision computations of divergent asymptotic series and homoclinic phenomena
- Unbounded energy growth in Hamiltonian systems with a slowly varying parameter
- Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem
- Some open problems in dynamical systems
- Regular and chaotic dynamics.
- KAM tori are very sticky: Rigorous lower bounds on the time to move away from an invariant Lagrangian torus with linear flow
- A \(\lambda\)-lemma for partially hyperbolic tori and the obstruction property
- Heteroclinic connections between periodic orbits in planar restricted circular three-body problem -- a computer-assisted proof
- Drift in phase space: A new variational mechanism with optimal diffusion time
- Superexponential stability of KAM tori.
- Wisdom system: dynamics in the adiabatic approximation
- Lectures on celestial mechanics. Transl. from the German by C. I. Kalme.
- 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 \(\mathbb{T}^2\)
- Is the solar system stable?
- Geometric properties of the scattering map of a normally hyperbolic invariant manifold
- Existence of diffusion orbits in a priori unstable Hamiltonian systems
- Transition tori in the planar restricted elliptic three-body problem
- Chaotic Evolution of the Solar System
- Introduction to the Perturbation Theory of Hamiltonian Systems
- An inclination lemma for normally hyperbolic manifolds with an application to diffusion
- 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
- Symbolic dynamics of almost collision orbits and skew products of symplectic maps
- Diffusion speed in the Mather problem
- KAM stability and celestial mechanics
- The dynamics of pseudographs in convex Hamiltonian systems
- Diffusion in Hamiltonian Quasi-Integrable Systems
- Stability over exponentially long times in the planetary problem
- 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
- Stable manifolds and the Perron–Irwin method
- SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS