Download or read book A Geometric Setting for Hamiltonian Perturbation Theory written by Anthony D. Blaom and published by American Mathematical Soc.. This book was released on 2001 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, the perturbation theory of non-commutatively integrable systems is revisited from the point of view of non-Abelian symmetry groups. Using a co-ordinate system intrinsic to the geometry of the symmetry, the book generalizes and geometrizes well-known estimates of Nekhoroshev (1977), in a class of systems having almost $G$-invariant Hamiltonians. These estimates are shown to have a natural interpretation in terms of momentum maps and co-adjoint orbits. The geometric framework adopted is described explicitly in examples, including the Euler-Poinsot rigid body.
Download or read book Geometric Perturbation Theory in Physics written by Stephen Malvern Omohundro and published by World Scientific. This book was released on 1986 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book which focusses on mechanics, waves and statistics, describes recent developments in the application of differential geometry, particularly symplectic geometry, to the foundations of broad areas of physics. Throughout the book, intuitive descriptions and diagrams are used to elucidate the mathematical theory. It develops a coordinate-free framework for perturbation theory and uses this to show how underlying symplectic structures arise from physical asymptotes. It describes a remarkable parity between classical mechanics which arises asymptotically from quantum mechanics and classical thermodynamics which arises asymptotically from statistical mechanics. Included here is a section with one hundred unanswered questions for further research.
Download or read book A Geometric Setting for Hamiltonian Jperturbation Theory written by Antohy D. Blaom and published by . This book was released on 2001 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to the Perturbation Theory of Hamiltonian Systems written by Dmitry Treschev and published by Springer Science & Business Media. This book was released on 2009-10-08 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an extended version of lectures given by the ?rst author in 1995–1996 at the Department of Mechanics and Mathematics of Moscow State University. We believe that a major part of the book can be regarded as an additional material to the standard course of Hamiltonian mechanics. In comparison with the original Russian 1 version we have included new material, simpli?ed some proofs and corrected m- prints. Hamiltonian equations ?rst appeared in connection with problems of geometric optics and celestial mechanics. Later it became clear that these equations describe a large classof systemsin classical mechanics,physics,chemistry,and otherdomains. Hamiltonian systems and their discrete analogs play a basic role in such problems as rigid body dynamics, geodesics on Riemann surfaces, quasi-classic approximation in quantum mechanics, cosmological models, dynamics of particles in an accel- ator, billiards and other systems with elastic re?ections, many in?nite-dimensional models in mathematical physics, etc. In this book we study Hamiltonian systems assuming that they depend on some parameter (usually?), where for?= 0 the dynamics is in a sense simple (as a rule, integrable). Frequently such a parameter appears naturally. For example, in celestial mechanics it is accepted to take? equal to the ratio: the mass of Jupiter over the mass of the Sun. In other cases it is possible to introduce the small parameter ar- ?cially.
Download or read book Spectral Decomposition of a Covering of GL r the Borel case written by Heng Sun and published by American Mathematical Soc.. This book was released on 2002 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $F$ be a number field and ${\bf A}$ the ring of adeles over $F$. Suppose $\overline{G({\bf A})}$ is a metaplectic cover of $G({\bf A})=GL(r, {\bf A})$ which is given by the $n$-th Hilbert symbol on ${\bf A}$
Download or read book Some Generalized Kac Moody Algebras with Known Root Multiplicities written by Peter Niemann and published by American Mathematical Soc.. This book was released on 2002 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from Borcherds' fake monster Lie algebra, this text construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for the root multiplicities of a number of hyperbolic Lie algebras, including $AE_3$.
Download or read book On the Classification of Polish Metric Spaces Up to Isometry written by Su Gao and published by American Mathematical Soc.. This book was released on 2003 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Derived ell Adic Categories for Algebraic Stacks written by Kai Behrend and published by American Mathematical Soc.. This book was released on 2003 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is intended for graduate students and research mathematicians interested in algebraic geometry, category theory and homological algebra.
Download or read book Triangulations of Oriented Matroids written by Francisco Santos and published by American Mathematical Soc.. This book was released on 2002 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the concept of triangulation of an oriented matroid. We provide a definition which generalizes the previous ones by Billera-Munson and by Anderson and which specializes to the usual notion of triangulation (or simplicial fan) in the realizable case. Then we study the relation existing between triangulations of an oriented matroid $\mathcal{M}$ and extensions of its dual $\mathcal{M}^*$, via the so-called lifting triangulations. We show that this duality behaves particularly well in the class of Lawrence matroid polytopes. In particular, that the extension space conjecture for realizable oriented matroids is equivalent to the restriction to Lawrence polytopes of the Generalized Baues problem for subdivisions of polytopes. We finish by showing examples and a characterization of lifting triangulations.
Download or read book The Rational Function Analogue of a Question of Schur and Exceptionality of Permutation Representations written by Robert M. Guralnick and published by American Mathematical Soc.. This book was released on 2003 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: Investigates the analogous question for rational functions. This book describes the Galois theoretic translation, based on Chebotarev's density theorem, leads to a certain property of permutation groups, called exceptionality.
Download or read book Connectivity Properties of Group Actions on Non Positively Curved Spaces written by Robert Bieri and published by American Mathematical Soc.. This book was released on 2003 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalizing the Bieri-Neumann-Strebel-Renz Invariants, this Memoir presents the foundations of a theory of (not necessarily discrete) actions $\rho$ of a (suitable) group $G$ by isometries on a proper CAT(0) space $M$. The passage from groups $G$ to group actions $\rho$ implies the introduction of 'Sigma invariants' $\Sigmak(\rho)$ to replace the previous $\Sigmak(G)$ introduced by those authors. Their theory is now seen as a special case of what is studied here so that readers seeking a detailed treatment of their theory will find it included here as a special case. We define and study 'controlled $k$-connectedness $(CCk)$' of $\rho$, both over $M$ and over end points $e$ in the 'boundary at infinity' $\partial M$; $\Sigmak(\rho)$ is by definition the set of all $e$ over which the action is $(k-1)$-connected. A central theorem, the Boundary Criterion, says that $\Sigmak(\rho) = \partial M$ if and only if $\rho$ is $CC{k-1}$ over $M$.An Openness Theorem says that $CCk$ over $M$ is an open condition on the space of isometric actions $\rho$ of $G$ on $M$. Another Openness Theorem says that $\Sigmak(\rho)$ is an open subset of $\partial M$ with respect to the Tits metric topology. When $\rho(G)$ is a discrete group of isometries the property $CC{k-1}$ is equivalent to ker$(\rho)$ having the topological finiteness property type '$F_k$'. More generally, if the orbits of the action are discrete, $CC{k-1}$ is equivalent to the point-stabilizers having type $F_k$. In particular, for $k=2$ we are characterizing finite presentability of kernels and stabilizers. Examples discussed include: locally rigid actions, translation actions on vector spaces (especially those by metabelian groups
Download or read book Gorenstein Liaison Complete Intersection Liaison Invariants and Unobstructedness written by Jan Oddvar Kleppe and published by American Mathematical Soc.. This book was released on 2001 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper contributes to the liaison and obstruction theory of subschemes in $\mathbb{P}^n$ having codimension at least three. The first part establishes several basic results on Gorenstein liaison. A classical result of Gaeta on liaison classes of projectively normal curves in $\mathbb{P}^3$ is generalized to the statement that every codimension $c$ ``standard determinantal scheme'' (i.e. a scheme defined by the maximal minors of a $t\times (t+c-1)$ homogeneous matrix), is in the Gorenstein liaison class of a complete intersection. Then Gorenstein liaison (G-liaison) theory is developed as a theory of generalized divisors on arithmetically Cohen-Macaulay schemes. In particular, a rather general construction of basic double G-linkage is introduced, which preserves the even G-liaison class. This construction extends the notion of basic double linkage, which plays a fundamental role in the codimension two situation. The second part of the paper studies groups which are invariant under complete intersection linkage, and gives a number of geometric applications of these invariants. Several differences between Gorenstein and complete intersection liaison are highlighted. For example, it turns out that linearly equivalent divisors on a smooth arithmetically Cohen-Macaulay subscheme belong, in general, to different complete intersection liaison classes, but they are always contained in the same even Gorenstein liaison class. The third part develops the interplay between liaison theory and obstruction theory and includes dimension estimates of various Hilbert schemes. For example, it is shown that most standard determinantal subschemes of codimension $3$ are unobstructed, and the dimensions of their components in the corresponding Hilbert schemes are computed.
Download or read book A Stability Index Analysis of 1 D Patterns of the Gray Scott Model written by A. Doelman and published by American Mathematical Soc.. This book was released on 2002 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is intended for graduate students and research mathematicians interested in partial differential equations.
Download or read book The Moduli Space of N 1 Superspheres with Tubes and the Sewing Operation written by Katrina Barron and published by American Mathematical Soc.. This book was released on 2003 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the framework of complex supergeometry and motivated by two-dimensional genus-zero holomorphic $N = 1$ superconformal field theory, this book defines the moduli space of $N=1$ genus-zero super-Riemann surfaces with oriented and ordered half-infinite tubes, modulo superconformal equivalence.
Download or read book Sub Laplacians with Drift on Lie Groups of Polynomial Volume Growth written by Georgios K. Alexopoulos and published by American Mathematical Soc.. This book was released on 2002 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is intended for graduate students and research mathematicians interested in topological groups, Lie groups, and harmonic analysis.
Download or read book Smooth Molecular Decompositions of Functions and Singular Integral Operators written by John E. Gilbert and published by American Mathematical Soc.. This book was released on 2002 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Under minimal assumptions on a function $\psi$ the authors obtain wavelet-type frames of the form $\psi_{j, k}(x) = r DEGREES{(1/2)n j} \psi(r DEGREESj x - sk), j \in \integer, k \in \integer DEGREESn, $ for some $r > 1$ and $s > 0$. This collection is shown to be a frame for a scale of Triebel-Lizorkin spaces (which includes Lebesgue, Sobolev and Hardy spaces) and the reproducing formula converges in norm as well as pointwise a.e. The construction follows from a characterization of those operators which are bounded on a space of smooth molecules. This characterization also allows us to decompose a broad range of singular integral operators in ter
Download or read book Generalized Whittaker Functions on SU 2 2 with Respect to the Siegel Parabolic Subgroup written by Yasuro Gon and published by American Mathematical Soc.. This book was released on 2002 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Obtains an explicit formula for generalized Whittaker functions and multiplicity one theorem for all discrete series representations of $SU(2,2)$.
