Download or read book Hamiltonian Perturbation Theory for Ultra Differentiable Functions written by Abed Bounemoura and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some scales of spaces of ultra-differentiable functions are introduced, having good stability properties with respect to infinitely many derivatives and compositions. They are well-suited for solving non-linear functional equations by means of hard implicit function theorems. They comprise Gevrey functions and thus, as a limiting case, analytic functions. Using majorizing series, we manage to characterize them in terms of a real sequence M bounding the growth of derivatives. In this functional setting, we prove two fundamental results of Hamiltonian perturbation theory: the invariant torus theorem, where the invariant torus remains ultra-differentiable under the assumption that its frequency satisfies some arithmetic condition which we call BRM, and which generalizes the Bruno-R¨ussmann condition; and Nekhoroshev’s theorem, where the stability time depends on the ultra-differentiable class of the pertubation, through the same sequence M. Our proof uses periodic averaging, while a substitute for the analyticity width allows us to bypass analytic smoothing. We also prove converse statements on the destruction of invariant tori and on the existence of diffusing orbits with ultra-differentiable perturbations, by respectively mimicking a construction of Bessi (in the analytic category) and MarcoSauzin (in the Gevrey non-analytic category). When the perturbation space satisfies some additional condition (we then call it matching), we manage to narrow the gap between stability hypotheses (e.g. the BRM condition) and instability hypotheses, thus circumbscribing the stability threshold. The formulas relating the growth M of derivatives of the perturbation on the one hand, and the arithmetics of robust frequencies or the stability time on the other hand, bring light to the competition between stability properties of nearly integrable systems and the distance to integrability. Due to our method of proof using width of regularity as a regularizing parameter, these formulas are closer to optimal as the the regularity tends to analyticity

Download or read book Instability Index Theorem and Exponential Trichotomy for Linear Hamiltonian PDEs written by Zhiwu Lin and published by American Mathematical Society. This book was released on 2022-02-02 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book Non Semisimple Extended Topological Quantum Field Theories written by Marco De Renzi and published by American Mathematical Society. This book was released on 2022-05-24 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two Parameter Generalization of the Riemann Zeta Function written by Athanassios S. Fokas and published by American Mathematical Society. This book was released on 2022-02-02 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book Elliptic Theory for Sets with Higher Co Dimensional Boundaries written by Guy David and published by American Mathematical Society. This book was released on 2021-12-30 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book Cell Complexes Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry written by Stuart Margolis and published by American Mathematical Society. This book was released on 2021-12-30 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book Cubic Action of a Rank One Group written by Matthias Grüninger and published by American Mathematical Society. This book was released on 2022-04-08 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book Local L p Brunn Minkowski Inequalities for p written by Alexander V. Kolesnikov and published by American Mathematical Society. This book was released on 2022-05-24 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book On the Symplectic Type of Isomorphisms of the p Torsion of Elliptic Curves written by Nuno Freitas and published by American Mathematical Society. This book was released on 2022-05-24 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book The Canonical Ring of a Stacky Curve written by John Voight and published by American Mathematical Society. This book was released on 2022-05-24 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book Souslin Quasi Orders and Bi Embeddability of Uncountable Structures written by Alessandro Andretta and published by American Mathematical Society. This book was released on 2022-05-24 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book Brownian Regularity for the Airy Line Ensemble and Multi Polymer Watermelons in Brownian Last Passage Percolation written by Alan Hammond and published by American Mathematical Society. This book was released on 2022-05-24 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book Positive Gaussian Kernels Also Have Gaussian Minimizers written by Franck Barthe and published by American Mathematical Society. This book was released on 2022-04-08 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book Isoperimetric Inequalities in Unbounded Convex Bodies written by Gian Paolo Leonardi and published by American Mathematical Society. This book was released on 2022-04-08 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book Tunneling Estimates and Approximate Controllability for Hypoelliptic Equations written by Camille Laurent and published by American Mathematical Society. This book was released on 2022-04-08 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book Maximal textrm PSL 2 Subgroups of Exceptional Groups of Lie Type written by David A. Craven and published by American Mathematical Society. This book was released on 2022-04-08 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book Abelian Networks IV Dynamics of Nonhalting Networks written by Swee Hong Chan and published by American Mathematical Society. This book was released on 2022-04-08 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.