Journal ArticleDOI
An exponential estimate of the time of stability of nearly-integrable hamiltonian systems
Reads0
Chats0
TLDR
The main ideas of the proof of the exponential estimate were discussed in this paper, including steepness conditions and forbidden motions of the discs of fast drift on the steepness of the unperturbed Hamiltonian.Abstract:
CONTENTS § 1 Introduction § 2 Unsolved problems Conjectures Generalizations § 3 The main ideas of the proof of the exponential estimate § 4 Steepness conditions Precise statement of the main theorem § 5 Forbidden motions § 6 Resonances Resonance zones and blocks § 7 Dependence of the diameters of the discs of fast drift on the steepness of the unperturbed Hamiltonian § 8 Condition for the non-overlapping of resonances § 9 Traps in frequency systems Completion of the proof of the main theorem § 10 Statement of the lemma on the elimination of non-resonance harmonics, and of the technical lemmas used in the proof of the main theorem § 11 Remarks on the proof of the main theorem § 12 Application of the main theorem to the many-body problem Referencesread more
Citations
More filters
Journal ArticleDOI
On the problem of stability for higher-order derivative Lagrangian systems
TL;DR: In this paper, the authors studied the stability of dynamical systems whose Lagrangian function depends on derivatives of a higher order than one, and showed that the indefiniteness of the energy does not forbid the stability.
Book ChapterDOI
Scaling Perspective on Intramolecular Vibrational Energy Flow: Analogies, Insights, and Challenges
TL;DR: In this article, the scaling approach to intramolecular vibrational energy flow emphasizing the classical-quantum correspondence perspective is described, and a review of the scaling approaches is presented.
Journal ArticleDOI
The production of Tsallis entropy in the limit of weak chaos and a new indicator of chaoticity
TL;DR: In this article, the average power law exponent (APLE) was proposed to distinguish regular from weakly chaotic trajectories, and applied to a wide range of properties of the Tsallis q-entropy.
Trends in 20th century Celestial Mechanics.
Takashi Ito,Kiyotaka Tanikawa +1 more
TL;DR: A review of the major achievements of celestial mechanics in the twentieth century, and some unsolved problems that are left to the twenty-first century can be found in this article, where four major research fields in celestial mechanics are treated: dynamical systems, three-body problems, solar system dynamics, and numerical methods.
Journal ArticleDOI
Beyond all orders: Singular perturbations in a mapping
TL;DR: In this paper, the authors consider a family of q-dimensional volume-preserving maps depending on a small parametere and show that for smalle the heteroclinic connection breaks up and that the splitting between its components scales with γexp[ −β/e.
References
More filters
Journal ArticleDOI
The applicability of the third integral of motion: Some numerical experiments
Michel Henon,Carl Heiles +1 more
TL;DR: In this paper, the existence of a third isolating integral of motion in an axisymmetric potential was investigated by numerical experiments and it was found that the third integral exists for only a limited rage of initial conditions.
Journal ArticleDOI
Small denominators and problems of stability of motion in classical and celestial mechanics
TL;DR: In this paper, the authors consider the problem of proper degeneracy and prove the existence of a non-degeneracy of diffeomorphisms with respect to a constant number of vertices.
Journal ArticleDOI
Proof of a theorem of a.?n.?kolmogorov on the invariance of quasi-periodic motions under small perturbations of the hamiltonian
TL;DR: In this paper, the rotatory motion of a heavy asymmetric rigid body is studied and the theorems of the rotational motion of such a rigid body are formulated and proved.