A. V. Bolsinov, A. T. Fomenko

Integrable Hamiltonian Systems (eBook, PDF)

Geometry, Topology, Classification

• Format: PDF

Produktbeschreibung

This volume describes and fully illustrates both the theory and applications of integrable Hamiltonian systems. Exploring the basic elements of Liouville functions and their singularities, it systematically classifies such systems for the case of integrable Hamiltonian systems with two degrees of freedom. It also describes the nontrivial connections between this theory and three-dimensional topology and gives a topological description of the behavior of integral trajectories under Liouville tori bifurcation. Integrable Hamiltonian Systems: Geometry, Topology, Classification will appeal to graduate students of mathematics and mathematicians working in the theory of dynamical systems and their applications.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 752
• Erscheinungstermin: 25. Februar 2004
• Englisch
• ISBN-13: 9780203643426
• Artikelnr.: 42564575

Autorenporträt

Bolsinov, A.V.; Fomenko, A.T.

Inhaltsangabe

Basic Notions. The Topology of Foliations on Two-Dimensional Surfaces
Generated by Morse Functions. Rough Liouville Equivalence of Integrable
Systems with Two Degrees of Freedom. Liouville Equivbalence of Integrable
Systems with Two Degrees of Freedom. Orbital Classification of Integrable
Systems with Two Degrees of Freedom. Classification of Hamiltonian Flows on
Two-Dimensional Surfaces up to Topological Conjugacy. Smooth Conjugacy of
Hamiltonian Flows on Two-Dimensional Surfaces. Orbital Classification of
Integrable Hamiltonian Systems with Two Degrees of Freedom. The Second
Step. Liouville Classification of Integrable Systems with Two Degrees of
Freedom in Four-Dimensional Neighborhoods of Singular Points. Methods of
Calculation of Topological Invariants of Integrable Hamiltonian Systems.
Integrable Geodesic Flows on Two-Dimensional Surfaces. Liouville
Classification of Integrable Geodesic Flows on Two-Dimensional Surfaces.
Orbital Classification of Integrable Geodesic Flows on Two-Dimensional
Surfaces. The Topology of Liouville Foliations in Classical Integrable
Cases in Rigid Body Dynamics. Maupertuis Principle and Geodesic
Equivalence.