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

Readership

Graduate students and research mathematicians working in ordinary and partial differential equations, dynamical systems, and mechanics.

Table of Contents

• V. P. Palamodov -- Stability of motion and algebraic geometry
• S. V. Bolotin -- Homoclinic orbits to invariant tori of Hamiltonian systems
• D. V. Treshchev -- An estimate of irremovable nonconstant terms in the reducibility problem
• D. V. Treshchev -- On the reducibility of the one-dimensional Schrödinger equation with quasi-periodic 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 two-segment trajectories of the Birkhoff billiards
• V. V. Kozlov -- Hydrodynamics of noncommutative integration of Hamiltonian systems
• V. V. Kozlov -- Problemata nova, ad quorum solutionem mathematici invitantur