Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations
Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations

Author: Jaume Llibre

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 206

ISBN-13: 082182581X

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This work presents a study of the foliations of the energy levels of a class of integrable Hamiltonian systems by the sets of constant energy and angular momentum. This includes a classification of the topological bifurcations and a dynamical characterization of the criticalleaves (separatrix surfaces) of the foliation. Llibre and Nunes then consider Hamiltonain perturbations of this class of integrable Hamiltonians and give conditions for the persistence of the separatrix structure of the foliations and for the existence of transversal ejection-collision orbits of the perturbed system. Finally, they consider a class of non-Hamiltonian perturbations of a family of integrable systems of the type studied earlier and prove the persistence of "almost all" the tori and cylinders that foliate the energy levels of the unperturbed system as a consequence of KAM theory.

Random Perturbations of Hamiltonian Systems
Random Perturbations of Hamiltonian Systems

Author: Mark Iosifovich Freĭdlin

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 97

ISBN-13: 0821825860

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Random perturbations of Hamiltonian systems in Euclidean spaces lead to stochastic processes on graphs, and these graphs are defined by the Hamiltonian. In the case of white-noise type perturbations, the limiting process will be a diffusion process on the graph. Its characteristics are expressed through the Hamiltonian and the characteristics of the noise. Freidlin and Wentzell calculate the process on the graph under certain conditions and develop a technique which allows consideration of a number of asymptotic problems. The Dirichlet problem for corresponding elliptic equations with a small parameter are connected with boundary problems on the graph.

Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations
Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations

Author: Jaume Llibre

Publisher:

Published: 2014-08-31

Total Pages: 206

ISBN-13: 9781470400903

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This work presents a study of the foliations of the energy levels of a class of integrable Hamiltonian systems by the sets of constant energy and angular momentum. This includes a classification of the topological bifurcations and a dynamical characterization of the criticalleaves (separatrix surfaces) of the foliation. Llibre and Nunes then consider Hamiltonain perturbations of this class of integrable Hamiltonians and give conditions for the persistence of the separatrix structure of the foliations and for the existence of transversal ejection-collision orbits of the perturbed system. Finally, they consider a class of non-Hamiltonian perturbations of a family of integrable systems of the type studied earlier and prove the persistence of almost all the tori and cylinders that foliate the energy levels of the unperturbed system as a consequence of KAM theory.

Higher Spinor Classes
Higher Spinor Classes

Author: J. F. Jardine

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 101

ISBN-13: 0821825909

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This work defines the higher spinor classes of an orthogonal representation of a Galois group. These classes are higher-degree analogues of the Fröhlich spinor class, which quantify the difference between the Stiefel-Whitney classes of an orthogonal representation and the Hasse-Witt classes of the associated form. Jardine establishes various basic properties, including vanishing in odd degrees and an induction formula for quadratic field extensions. The methods used include the homotopy theory of simplicial presheaves and the action of the Steenrod algebra on mod 2 étale cohomology.

Hamiltonian Systems And Celestial Mechanics (Hamsys-98) - Proceedings Of The Iii International Symposium
Hamiltonian Systems And Celestial Mechanics (Hamsys-98) - Proceedings Of The Iii International Symposium

Author: J Delgado

Publisher: World Scientific

Published: 2000-10-09

Total Pages: 373

ISBN-13: 9814492116

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This volume is an outgrowth of the Third International Symposium on Hamiltonian Systems and Celestial Mechanics. The main topics are Arnold diffusion, central configurations, singularities in few-body problems, billiards, area-preserving maps, and geometrical mechanics. All papers in the volume went through the refereeing process typical of a mathematical research journal.

The Index Theorem for Minimal Surfaces of Higher Genus
The Index Theorem for Minimal Surfaces of Higher Genus

Author: Friedrich Tomi

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 90

ISBN-13: 0821803522

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In this paper we formulate and prove an index theorem for minimal surfaces of higher topological type spanning one boundary contour. Our techniques carry over to surfaces with several boundary contours as well as to unoriented surfaces.

Hamiltonian Systems and Celestial Mechanics
Hamiltonian Systems and Celestial Mechanics

Author:

Publisher: World Scientific

Published: 2000

Total Pages: 380

ISBN-13: 9789810244637

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This volume is an outgrowth of the Third International Symposium on Hamiltonian Systems and Celestial Mechanics. The main topics are Arnold diffusion, central configurations, singularities in few-body problems, billiards, area-preserving maps, and geometrical mechanics. All papers in the volume went through the refereeing process typical of a mathematical research journal.

Some Special Properties of the Adjunction Theory for $3$-Folds in $\mathbb P^5$
Some Special Properties of the Adjunction Theory for $3$-Folds in $\mathbb P^5$

Author: Mauro Beltrametti

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 79

ISBN-13: 0821802348

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This work studies the adjunction theory of smooth 3-folds in P]5. Because of the many special restrictions on such 3-folds, the structure of the adjunction theoretic reductions are especially simple, e.g. the 3-fold equals its first reduction, the second reduction is smooth except possibly for a few explicit low degrees, and the formulae relating the projective invariants of the given 3-fold with the invariants of its second reduction are very explicit. Tables summarizing the classification of such 3-folds up to degree 12 are included. Many of the general results are shown to hold for smooth projective n-folds embedded in P]N with N 2n -1.

An Extension of the Galois Theory of Grothendieck
An Extension of the Galois Theory of Grothendieck

Author: André Joyal

Publisher: American Mathematical Soc.

Published: 1984

Total Pages: 87

ISBN-13: 0821823124

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In this paper we compare, in a precise way, the concept of Grothendieck topos to the classical notion of topological space. The comparison takes the form of a two-fold extension of the idea of space.