On a notion of weak stability and its relevance for celestial mechanics and molecular dynamics View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1994

AUTHORS

Luigi Galgani , Antonio Giorgilli

ABSTRACT

The stability problem in Hamiltonian dynamics is discussed in the light of Nekhoroshev's theorem. This guarantees a form of weak stability, namely referred to finite (rather than infinite) times. Applications are discussed for the restricted problem of three bodies and for the problem of energy equipartition in statistical mechanics.

PAGES

56-63

References to SciGraph publications

  • 1984-10. Boltzmann's ultraviolet cutoff and Nekhoroshev's theorem on Arnold diffusion in NATURE
  • 1988-09. Estimates for normal forms of differential equations near an equilibrium point in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • 1988. Relaxation Times and the Foundations of Classical Statistical Mechanics in the Light of Modern Perturbation Theory in NONLINEAR EVOLUTION AND CHAOTIC PHENOMENA
  • 1986-08. Stability of motions near resonances in quasi-integrable Hamiltonian systems in JOURNAL OF STATISTICAL PHYSICS
  • 1988. Relevance of Exponentially Large Time Scales in Practical Applications: Effective Fractal Dimensions in Conservative Dynamical Systems in NONLINEAR EVOLUTION AND CHAOTIC PHENOMENA
  • 1990-03. On the stability of the lagrangian points in the spatial restricted problem of three bodies in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1985-09. A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1989-12. Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part II in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1987-03. Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part I in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1895-02. On Certain Questions of the Theory of Gases in NATURE
  • 1993-05. Exponential stability of states close to resonance in infinite-dimensional Hamiltonian systems in JOURNAL OF STATISTICAL PHYSICS
  • 1992-11. Towards a rigorous treatment of the Jeans-Landau-Teller method for the energy exchanges of harmonic oscillators in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1988. Nekhoroshev-Like Results for Hamiltonian Dynamical Systems in NONLINEAR EVOLUTION AND CHAOTIC PHENOMENA
  • Book

    TITLE

    Ergodic Concepts in Stellar Dynamics

    ISBN

    3-540-57929-X

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bfb0058090

    DOI

    http://dx.doi.org/10.1007/bfb0058090

    DIMENSIONS

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