Chirikov and Nekhoroshev diffusion estimates: bridging the two sides of the river

DOI10.1016/j.physd.2013.10.005zbMath1286.37059arXiv1310.3158OpenAlexW1984067731WikidataQ98636435 ScholiaQ98636435MaRDI QIDQ2448682

Martín F. Mestre, Christos Efthymiopoulos, Pablo M. Cincotta, Claudia M. Giordano

Publication date: 5 May 2014

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.3158

zbMATH Keywords

chaosdynamicsArnold diffusioninstabilitiesNekhoroshev's and Chirikov's diffusion theories

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Nonlinear resonances for nonlinear problems in mechanics (70K30) Nearly integrable Hamiltonian systems, KAM theory (70H08) Normal forms for nonlinear problems in mechanics (70K45)

Related Items

The Nekhoroshev theorem and the observation of long-term diffusion in Hamiltonian systems ⋮ Quantum kicked rotor and its variants: chaos, localization and beyond ⋮ Semi-analytic computations of the speed of Arnold diffusion along single resonances in a priori stable Hamiltonian systems ⋮ Semi-analytical estimates for the chaotic diffusion in the second fundamental model of resonance. Application to Earth's navigation satellites ⋮ Diffusion and drift in volume-preserving maps ⋮ On the chaotic diffusion in multidimensional Hamiltonian systems ⋮ Phase correlations in chaotic dynamics: a Shannon entropy measure ⋮ Shannon entropy applied to the planar restricted three-body problem ⋮ The Shannon entropy as a measure of diffusion in multidimensional dynamical systems ⋮ Shannon entropy diffusion estimates: sensitivity on the parameters of the method ⋮ Arnold web and dynamical tunneling in a four-site Bose-Hubbard model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The speed of Arnold diffusion
• Chirikov diffusion in the asteroidal three-body resonance \((5, - 2, - 2)\)
• On the role of high order resonances in normal forms and in separatrix splitting
• Local and global diffusion along resonant lines in discrete quasi-integrable dynamical systems
• Canonical perturbation theories. Degenerate systems and resonance
• A numerical study of the size of the homoclinic tangle of hyperbolic tori and its correlation with Arnold diffusion in Hamiltonian systems
• A numerical study of the hyperbolic manifolds in a priori unstable systems. A comparison with Melnikov approximations
• Resonance transport in near-integrable systems with many degrees of freedom
• On the connection between the Nekhoroshev theorem and Arnold diffusion
• The separation of motions in systems with rapidly rotating phase
• Frequency analysis for multi-dimensional systems. Global dynamics and diffusion
• Nekhoroshev estimates for quasi-convex Hamiltonian systems
• Structures in the phase space of a four dimensional symplectic map
• Phase space structure of multi-dimensional systems by means of the mean exponential growth factor of nearby orbits
• Detection of Arnold diffusion in Hamiltonian systems
• High-order symplectic integration: An assessment
• The production of Tsallis entropy in the limit of weak chaos and a new indicator of chaoticity
• First numerical evidence of global Arnold diffusion in quasi-integrable systems
• Measure of the exponential splitting of the homoclinic tangle in four-dimensional symplectic mappings
• Special Features of Galactic Dynamics
• A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems
• AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS
• Complex analysis and convolution operators
• Alignment indices: a new, simple method for determining the ordered or chaotic nature of orbits
• Nonconvergence of formal integrals: II. Improved estimates for the optimal order of truncation
• Diffusion and stability in perturbed non-convex integrable systems
• On the relationship between fast Lyapunov indicator and periodic orbits for symplectic mappings

This page was built for publication: Chirikov and Nekhoroshev diffusion estimates: bridging the two sides of the river