Hardcover ISBN:  9780821804278 
Product Code:  TRANS2/168 
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eBook ISBN:  9781470433796 
Product Code:  TRANS2/168.E 
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AMS Member Price:  $132.00 
Hardcover ISBN:  9780821804278 
eBook: ISBN:  9781470433796 
Product Code:  TRANS2/168.B 
List Price:  $340.00 $257.50 
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Hardcover ISBN:  9780821804278 
Product Code:  TRANS2/168 
List Price:  $175.00 
MAA Member Price:  $157.50 
AMS Member Price:  $140.00 
eBook ISBN:  9781470433796 
Product Code:  TRANS2/168.E 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
Hardcover ISBN:  9780821804278 
eBook ISBN:  9781470433796 
Product Code:  TRANS2/168.B 
List Price:  $340.00 $257.50 
MAA Member Price:  $306.00 $231.75 
AMS Member Price:  $272.00 $206.00 

Book DetailsAmerican Mathematical Society Translations  Series 2Advances in the Mathematical SciencesVolume: 168; 1995; 254 ppMSC: Primary 34; 58; 70; 78; Secondary 14; 35; 76
This book shows that the phenomenon of integrability is related not only to Hamiltonian systems, but also to a wider variety of systems having invariant measures that often arise in nonholonomic mechanics. Each paper presents unique ideas and original approaches to various mathematical problems related to integrability, stability, and chaos in classical dynamics.
Topics include...
 the inverse Lyapunov theorem on stability of equilibria
 geometrical aspects of Hamiltonian mechanics from a hydrodynamic perspective
 current unsolved problems in the dynamical systems approach to classical mechanics
ReadershipGraduate students and research mathematicians working in ordinary and partial differential equations, dynamical systems, and mechanics.

Table of Contents

Chapters

Valery V. Kozlov — Introduction

V. P. Palamodov — Stability of motion and algebraic geometry

Sergey V. Bolotin — Homoclinic orbits to invariant tori of Hamiltonian systems

Dmitry V. Treshchev — An estimate of irremovable nonconstant terms in the reducibility problem

Dmitry V. Treshchev — On the reducibility of the onedimensional Schrödinger equation with quasiperiodic potential

Yu. N. Fedorov and V. V. Kozlov — Various aspects of $n$dimensional rigid body dynamics

Yu. N. Fedorov — Integrable systems, Lax representations, and confocal quadrics

N. G. Moshchevitin — Recent results on asymptotic behavior of integrals of quasiperiodic functions

A. A. Markeev — The method of pointwise mappings in the stability problem of twosegment trajectories of the Birkhoff billiards

Valery V. Kozlov — Hydrodynamics of noncommutative integration of Hamiltonian systems

Valery V. Kozlov — Problemata nova, ad quorum solutionem mathematici invitantur


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This book shows that the phenomenon of integrability is related not only to Hamiltonian systems, but also to a wider variety of systems having invariant measures that often arise in nonholonomic mechanics. Each paper presents unique ideas and original approaches to various mathematical problems related to integrability, stability, and chaos in classical dynamics.
Topics include...
 the inverse Lyapunov theorem on stability of equilibria
 geometrical aspects of Hamiltonian mechanics from a hydrodynamic perspective
 current unsolved problems in the dynamical systems approach to classical mechanics
Graduate students and research mathematicians working in ordinary and partial differential equations, dynamical systems, and mechanics.

Chapters

Valery V. Kozlov — Introduction

V. P. Palamodov — Stability of motion and algebraic geometry

Sergey V. Bolotin — Homoclinic orbits to invariant tori of Hamiltonian systems

Dmitry V. Treshchev — An estimate of irremovable nonconstant terms in the reducibility problem

Dmitry V. Treshchev — On the reducibility of the onedimensional Schrödinger equation with quasiperiodic potential

Yu. N. Fedorov and V. V. Kozlov — Various aspects of $n$dimensional rigid body dynamics

Yu. N. Fedorov — Integrable systems, Lax representations, and confocal quadrics

N. G. Moshchevitin — Recent results on asymptotic behavior of integrals of quasiperiodic functions

A. A. Markeev — The method of pointwise mappings in the stability problem of twosegment trajectories of the Birkhoff billiards

Valery V. Kozlov — Hydrodynamics of noncommutative integration of Hamiltonian systems

Valery V. Kozlov — Problemata nova, ad quorum solutionem mathematici invitantur