A Geometric Setting for Hamiltonian Perturbation Theory
Title | A Geometric Setting for Hamiltonian Perturbation Theory PDF eBook |
Author | Anthony D. Blaom |
Publisher | American Mathematical Soc. |
Pages | 137 |
Release | 2001 |
Genre | Mathematics |
ISBN | 0821827200 |
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.
Geometric Perturbation Theory in Physics
Title | Geometric Perturbation Theory in Physics PDF eBook |
Author | Stephen Malvern Omohundro |
Publisher | World Scientific |
Pages | 594 |
Release | 1986 |
Genre | Science |
ISBN | 9789971501365 |
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.
A Geometric Setting for Hamiltonian Jperturbation Theory
Title | A Geometric Setting for Hamiltonian Jperturbation Theory PDF eBook |
Author | Antohy D. Blaom |
Publisher | |
Pages | 122 |
Release | 2001 |
Genre | |
ISBN |
Elliptic Partial Differential Operators and Symplectic Algebra
Title | Elliptic Partial Differential Operators and Symplectic Algebra PDF eBook |
Author | William Norrie Everitt |
Publisher | American Mathematical Soc. |
Pages | 130 |
Release | 2003 |
Genre | Mathematics |
ISBN | 0821832352 |
This investigation introduces a new description and classification for the set of all self-adjoint operators (not just those defined by differential boundary conditions) which are generated by a linear elliptic partial differential expression $A(\mathbf{x}, D)=\sum_{0\, \leq\, \left s\right \, \leq\,2m}a_{s} (\mathbf{x})D DEGREES{s}\;\text{for all}\;\mathbf{x}\in\Omega$ in a region $\Omega$, with compact closure $\overline{\Omega}$ and $C DEGREES{\infty }$-smooth boundary $\partial\Omega$, in Euclidean space $\mathbb{E} DEGREES{r}$ $(r\geq2).$ The order $2m\geq2$ and the spatial dimensio
Basic Global Relative Invariants for Homogeneous Linear Differential Equations
Title | Basic Global Relative Invariants for Homogeneous Linear Differential Equations PDF eBook |
Author | Roger Chalkley |
Publisher | American Mathematical Soc. |
Pages | 223 |
Release | 2002 |
Genre | Mathematics |
ISBN | 0821827812 |
Given any fixed integer $m \ge 3$, the author presents simple formulas for $m - 2$ algebraically independent polynomials over $\mathbb{Q}$ having the remarkable property, with respect to transformations of homogeneous linear differential equations of order $m$, that each polynomial is both a semi-invariant of the first kind (with respect to changes of the dependent variable) and a semi-invariant of the second kind (with respect to changes of the independent variable). These relative invariants are suitable for global studies in several different contexts and do not require Laguerre-Forsyth reductions for their evaluation. In contrast, all of the general formulas for basic relative invariants that have been proposed by other researchers during the last 113 years are merely local ones that are either much too complicated or require a Laguerre-Forsyth reduction for each evaluation.
Spectral Decomposition of a Covering of $GL(r)$: the Borel case
Title | Spectral Decomposition of a Covering of $GL(r)$: the Borel case PDF eBook |
Author | Heng Sun |
Publisher | American Mathematical Soc. |
Pages | 79 |
Release | 2002 |
Genre | Mathematics |
ISBN | 0821827758 |
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 ${\bf A}$
Limit Theorems for Null Recurrent Markov Processes
Title | Limit Theorems for Null Recurrent Markov Processes PDF eBook |
Author | Reinhard Höpfner |
Publisher | American Mathematical Soc. |
Pages | 105 |
Release | 2003 |
Genre | Mathematics |
ISBN | 082183231X |