Separatrix Surfaces And Invariant Manifolds Of A Class Of Integrable Hamiltonian Systems And Their Perturbations

Author : Jaume Llibre,Ana Nunes
Publisher : American Mathematical Soc.
Page : 191 pages
File Size : 54,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825815

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Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations by Jaume Llibre,Ana Nunes Pdf

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 critical leaves (separatrix surfaces) of the foliation. Llibre and Nunes then consider Hamiltonian 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.

Author : Jaume Llibre
Publisher : Unknown
Page : 206 pages
File Size : 40,5 Mb
Release : 2014-08-31
Category : MATHEMATICS
ISBN : 1470400901

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Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations by Jaume Llibre Pdf

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.

Author : Mark Iosifovich Freĭdlin,Alexander D. Wentzell
Publisher : American Mathematical Soc.
Page : 82 pages
File Size : 48,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825860

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Random Perturbations of Hamiltonian Systems by Mark Iosifovich Freĭdlin,Alexander D. Wentzell Pdf

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.

Author : J. F. Jardine
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 40,6 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825907

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Higher Spinor Classes by J. F. Jardine Pdf

This work defines the higher spinor classes of an orthogonal representation of a Galois group. These classes are higher-degree analogues of the Frohlich 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 etale cohomology.

Author : J Delgado,E A Lacomba,E Pérez-Chavela,J Llibre
Publisher : World Scientific
Page : 370 pages
File Size : 53,8 Mb
Release : 2000-10-09
Category : Science
ISBN : 9789814492119

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Hamiltonian Systems and Celestial Mechanics by J Delgado,E A Lacomba,E Pérez-Chavela,J Llibre Pdf

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. Contents:The Rhomboidal Charged Four Body Problem (F Alfaro & E Pérez-Chavela)Planetary Rings with Shepherds (L Benet & T H Seligman)Low Reynolds Number Swimming in Two Dimensions (A Cherman et al.)2-Dimensional Invariant Tori for the Spatial Isosceles 3-Body Problem (M Corbera & J Llibre)The Global Flow for the Synodical Spatial Kepler Problem (M P Dantas & J Llibre)Unbounded Growth of Energy in Periodic Perturbations of Geodesic Flows of the Torus (A Delshams et al.)Splitting and Melnikov Potentials in Hamiltonian Systems (A Delshams & P Gutiérrez)Infinity Manifolds of Cubic Polynomial Hamiltonian Vector Fields with 2 Degrees of Freedom (M Falconi et al.)Relativistic Corrections to Elementary Galilean Dynamics and Deformations of Poisson Brackets (R Flores-Espinoza & Y M Vorobjev)Heteroclinic Phenomena in the Sitnikov Problem (A García & E Pérez-Chavela)Doubly-Symmetric Periodic Solutions of Hill's Lunar Problem (R C Howison & K R Meyer)On Practical Stability Regions for the Motion of a Small Particle Close to the Equilateral Points of the Real Earth-Moon System (À Jorba)Variational Methods for Quasi-Periodic Solutions of Partial Differential Equations (R de la Llave)The Splitting of Invariant Lagrangian Submanifolds: Geometry and Dynamics (J-P Marco)Cross-Sections in the Planar N-Body Problem (C McCord)Existence of an Additional First Integral and Completeness of the Flow for Hamiltonian Vector Fields (J Muciño-Raymundo)Simplification of Perturbed Hamiltonians Through Lie Transformations (J Palacián & P Yanguas)Linear Stability in the 1 + N-Gon Relative Equilibrium (G E Roberts)Analytic Continuation of Circular and Elliptic Kepler Motion to the General 3-Body Problem (J Soler)The Phase Space of Finite Systems (K B Wolf et al.) Readership: Students and researchers in mathematics and nonlinear dynamics. Keywords:Charged Four Body Problem;Low Reynolds Number;Relativistic Corrections;Sitnikov Problem;Hill's Lunar Problem;Invariant Lagrangian Submanifolds;Planar N-Body Problem;Elliptic Kepler Motion

Author : Friedrich Tomi,Anthony Tromba
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 48,6 Mb
Release : 1995
Category : Index theorems
ISBN : 9780821803523

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The Index Theorem for Minimal Surfaces of Higher Genus by Friedrich Tomi,Anthony Tromba Pdf

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.

Author : Anonim
Publisher : World Scientific
Page : 380 pages
File Size : 43,6 Mb
Release : 2000
Category : Mathematics
ISBN : 9810244630

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Hamiltonian Systems and Celestial Mechanics by Anonim Pdf

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.

Author : Mauro Beltrametti,Michael Schneider,Andrew John Sommese
Publisher : American Mathematical Soc.
Page : 79 pages
File Size : 52,6 Mb
Release : 1995
Category : Adjunction theory
ISBN : 9780821802342

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Some Special Properties of the Adjunction Theory for $3$-Folds in $\mathbb P^5$ by Mauro Beltrametti,Michael Schneider,Andrew John Sommese Pdf

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.

Author : Victor Guillemin,Shlomo Sternberg
Publisher : American Mathematical Soc.
Page : 80 pages
File Size : 40,6 Mb
Release : 1966
Category : Mathematics
ISBN : 9780821812648

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Deformation Theory of Pseudogroup Structures by Victor Guillemin,Shlomo Sternberg Pdf

Author : André Joyal,Myles Tierney
Publisher : American Mathematical Soc.
Page : 71 pages
File Size : 45,5 Mb
Release : 1984
Category : Mathematics
ISBN : 9780821823125

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An Extension of the Galois Theory of Grothendieck by André Joyal,Myles Tierney Pdf

Author : Eric M. Friedlander,Barry Mazur
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 51,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825914

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Filtrations on the Homology of Algebraic Varieties by Eric M. Friedlander,Barry Mazur Pdf

This work provides a detailed exposition of a classical topic from a very recent viewpoint. Friedlander and Mazur describe some foundational aspects of ``Lawson homology'' for complex projective algebraic varieties, a homology theory defined in terms of homotopy groups of spaces of algebraic cycles. Attention is paid to methods of group completing abelian topological monoids. The authors study properties of Chow varieties, especially in connection with algebraic correspondences relating algebraic varieties. Operations on Lawson homology are introduced and analyzed. These operations lead to a filtration on the singular homology of algebraic varieties, which is identified in terms of correspondences and related to classical filtrations of Hodge and Grothendieck.

Author : Robert Gordon,Anthony John Power,Ross Street
Publisher : American Mathematical Soc.
Page : 81 pages
File Size : 49,9 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803448

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Coherence for Tricategories by Robert Gordon,Anthony John Power,Ross Street Pdf

The need to address the appropriate three-dimensional generalization of category (tricategory) has been felt in homotopy theory, low-dimensional topology, cohomology theory, category theory, and quantum field theory. Benabou's bicategories provide the two-dimensional notion into which examples naturally fit. In developing the theory of bicategories it is very reassuring to know the coherence theorem: They can be replaced by the stricter 2-categories which are merely categories enriched in the category of categories. In this book, the authors provide ... the unique source of the full definition of tricategory a thorough and complete proof of the coherence theorem for tricategories a wholly modern source of material on Gray's tensor product of 2-categories

Author : Paul S. Muhly,Baruch Solel
Publisher : American Mathematical Soc.
Page : 53 pages
File Size : 47,7 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803462

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Hilbert Modules over Operator Algebras by Paul S. Muhly,Baruch Solel Pdf

This book gives a general systematic analysis of the notions of ``projectivity'' and ``injectivity'' in the context of Hilbert modules over operator algebras. A Hilbert module over an operator algebra $A$ is simply the Hilbert space of a (contractive) representation of $A$ viewed as a module over $A$ in the usual way. In this work, Muhly and Solel introduce various notions of projective Hilbert modules and use them to investigate dilation and commutant lifting problems over certain infinite dimensional analogues of incidence algebras. The authors prove that commutant lifting holds for such an algebra if and only if the pattern indexing the algebra is a ``tree'' in the sense of computer directories.

Author : Lev M. Lerman
Publisher : American Mathematical Soc.
Page : 58 pages
File Size : 47,9 Mb
Release : 2000
Category : Mathematics
ISBN : 0821826638

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Methods of Qualitative Theory of Differential Equations and Related Topics by Lev M. Lerman Pdf

Dedicated to the memory of Professor E. A. Leontovich-Andronova, this book was composed by former students and colleagues who wished to mark her contributions to the theory of dynamical systems. A detailed introduction by Leontovich-Andronova's close colleague, L. Shilnikov, presents biographical data and describes her main contribution to the theory of bifurcations and dynamical systems. The main part of the volume is composed of research papers presenting the interests of Leontovich-Andronova, her students and her colleagues. Included are articles on traveling waves in coupled circle maps, bifurcations near a homoclinic orbit, polynomial quadratic systems on the plane, foliations on surfaces, homoclinic bifurcations in concrete systems, topology of plane controllability regions, separatrix cycle with two saddle-foci, dynamics of 4-dimensional symplectic maps, torus maps from strong resonances, structure of 3 degree-of-freedom integrable Hamiltonian systems, splitting separatrices in complex differential equations, Shilnikov's bifurcation for C1-smooth systems and "blue sky catastrophe" for periodic orbits.

Author : John Lindsay Orr
Publisher : American Mathematical Soc.
Page : 49 pages
File Size : 54,9 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804056

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Triangular Algebras and Ideals of Nest Algebras by John Lindsay Orr Pdf

Triangular algebras and nest algebras are two important classes of non-selfadjoint operator algebras. In this book, the author uses the new depth of understanding which the similarity theory for nests has opened up to study ideals of nest algebras. In particular, a unique largest diagonal-disjoint ideal is identified for each nest algebra. Using a construction proposed by Kadison and Singer, this ideal can be used to construct new maximal triangular algebras. These new algebras are the first concrete descriptions of maximal triangular algebras that are not nest algebras.