Ebook: Seminar on Dynamical Systems: Euler International Mathematical Institute, St. Petersburg, 1991

The "Dynamical Systems Semester" took place at the Euler International Mathematical Institute in St. Petersburg, Russia, in the autumn of 1991. There were two workshops, October 14-25 and November 18-29, with more than 60 participants giving 70 talks. The titles of all talks are given at the end of this volume. Here we included 22 papers prepared by the authors especially for this volume, while the material of the other talks are published elsewhere. The semester was sponsored by the Soviet Academy of Sciences and UN­ ESCO. Since the new building of the Euler Institute was not ready at that moment, the sessions were held in the old building of the Steklov Mathemati­ cal Institute in the very center of St. Petersburg. Members of the staff of the Euler Institute were doing their best to organize properly the normal processing of the conference-not a simple task at that time because of the complications in the political and economical life in Russia just between the coup d'etat in August and the dismantling of the Soviet Union in December. We are thankful to all of them.

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Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
The Dynamical Foundations of Classical Statistical Mechanics and the Boltzmann-Jeans Conjecture....Pages 3-14
Stability of Nearly Integrable Convex Hamiltonian Systems Over Exponentially Long Times....Pages 15-34
On the Stability Problem for Nearly-Integrable Hamiltonian Systems....Pages 35-46
Separatrices Splitting for the Rapidly Forced Pendulum....Pages 47-67
Exponentially Small Expressions for Separatrix Splittings....Pages 68-80
An Unusual Variational Problem Connected with Mather’s Theory for Monotone Twist Mappings....Pages 81-89
Periodic Metrics....Pages 90-95
On the Inclusion of Analytic Symplectic Maps in Analytic Hamiltonian Flows and Its Applications....Pages 96-116
Poincaré Compactification of the Kepler and the Collinear Three Body Problems....Pages 117-128
A Note on the Existence of Heteroclinic Orbits in the Planar Three-Body Problem....Pages 129-139
Kam Tori for Modulated Symplectic Maps....Pages 140-153
Analyticty of Normalizing Transformations for Area Preserving Maps....Pages 154-159
On the Frequencies of Quasi Periodic Solutions of Analytic Nearly Integrable Hamiltonian Systems....Pages 160-183
New Results in the Reversible Kam Theory....Pages 184-199
Front Matter....Pages 201-201
Maximal Almost-Periodic Solutions for Lagrangian Equations on Infinite Dimensional Tori....Pages 203-212
Nonpersistence of Breather Solutions under Perturbation of the Sine-Gordon Equation....Pages 213-224
Front Matter....Pages 225-225
Attractors, Integrable Hamiltonian Systems and the Reidemeister Torsion....Pages 227-234
Linear Connections for Hamiltonian Dynamics over Isotropic Submanifold....Pages 235-252
Four-Dimensional Integrable Hamiltonian Systems with Simple Singular Points....Pages 253-260
The Periodic Points and Symbolic Dynamics....Pages 261-267
Front Matter....Pages 225-225
On the Perturbation of Invariant Manifolds....Pages 268-276
Complex Geometry of the Billiard on the Ellipsoid and Quasicrystallic Curves....Pages 277-283
Back Matter....Pages 285-292

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Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
The Dynamical Foundations of Classical Statistical Mechanics and the Boltzmann-Jeans Conjecture....Pages 3-14
Stability of Nearly Integrable Convex Hamiltonian Systems Over Exponentially Long Times....Pages 15-34
On the Stability Problem for Nearly-Integrable Hamiltonian Systems....Pages 35-46
Separatrices Splitting for the Rapidly Forced Pendulum....Pages 47-67
Exponentially Small Expressions for Separatrix Splittings....Pages 68-80
An Unusual Variational Problem Connected with Mather’s Theory for Monotone Twist Mappings....Pages 81-89
Periodic Metrics....Pages 90-95
On the Inclusion of Analytic Symplectic Maps in Analytic Hamiltonian Flows and Its Applications....Pages 96-116
Poincaré Compactification of the Kepler and the Collinear Three Body Problems....Pages 117-128
A Note on the Existence of Heteroclinic Orbits in the Planar Three-Body Problem....Pages 129-139
Kam Tori for Modulated Symplectic Maps....Pages 140-153
Analyticty of Normalizing Transformations for Area Preserving Maps....Pages 154-159
On the Frequencies of Quasi Periodic Solutions of Analytic Nearly Integrable Hamiltonian Systems....Pages 160-183
New Results in the Reversible Kam Theory....Pages 184-199
Front Matter....Pages 201-201
Maximal Almost-Periodic Solutions for Lagrangian Equations on Infinite Dimensional Tori....Pages 203-212
Nonpersistence of Breather Solutions under Perturbation of the Sine-Gordon Equation....Pages 213-224
Front Matter....Pages 225-225
Attractors, Integrable Hamiltonian Systems and the Reidemeister Torsion....Pages 227-234
Linear Connections for Hamiltonian Dynamics over Isotropic Submanifold....Pages 235-252
Four-Dimensional Integrable Hamiltonian Systems with Simple Singular Points....Pages 253-260
The Periodic Points and Symbolic Dynamics....Pages 261-267
Front Matter....Pages 225-225
On the Perturbation of Invariant Manifolds....Pages 268-276
Complex Geometry of the Billiard on the Ellipsoid and Quasicrystallic Curves....Pages 277-283
Back Matter....Pages 285-292
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