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Author: Kazuyuki Hatada
Publisher: American Mathematical Soc.
ISBN: 1470443341
Category : Education
Languages : en
Pages : 165
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Author: Kazuyuki Hatada
Publisher: American Mathematical Soc.
ISBN: 1470443341
Category : Education
Languages : en
Pages : 165
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Book Description
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Author: Mark Pollicott
Publisher: American Mathematical Society
ISBN: 1470465779
Category : Mathematics
Languages : en
Pages : 139
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Author: Abed Bounemoura
Publisher: American Mathematical Soc.
ISBN: 147044691X
Category : Education
Languages : en
Pages : 89
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Book Description
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
Author: Yurii Kolomoitsev
Publisher: American Mathematical Society
ISBN: 1470447584
Category : Mathematics
Languages : en
Pages : 118
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Author: Cheol-Hyun Cho
Publisher: American Mathematical Society
ISBN: 1470447614
Category : Mathematics
Languages : en
Pages : 116
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Author: Christian Haase
Publisher: American Mathematical Soc.
ISBN: 1470447169
Category : Education
Languages : en
Pages : 83
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Unimodular triangulations of lattice polytopes arise in algebraic geometry, commutative algebra, integer programming and, of course, combinatorics. In this article, we review several classes of polytopes that do have unimodular triangulations and constructions that preserve their existence. We include, in particular, the first effective proof of the classical result by Knudsen-Mumford-Waterman stating that every lattice polytope has a dilation that admits a unimodular triangulation. Our proof yields an explicit (although doubly exponential) bound for the dilation factor.
Author: Sebastian Throm
Publisher: American Mathematical Society
ISBN: 147044786X
Category : Mathematics
Languages : en
Pages : 106
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Author: Thorsten Heidersdorf
Publisher: American Mathematical Soc.
ISBN: 1470447142
Category : Education
Languages : en
Pages : 106
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We define and study cohomological tensor functors from the category Tn of finite-dimensional representations of the supergroup Gl(n|n) into Tn−r for 0 < r ≤ n. In the case DS : Tn → Tn−1 we prove a formula DS(L) = ΠniLi for the image of an arbitrary irreducible representation. In particular DS(L) is semisimple and multiplicity free. We derive a few applications of this theorem such as the degeneration of certain spectral sequences and a formula for the modified superdimension of an irreducible representation.
Author: William Gignac
Publisher: American Mathematical Society
ISBN: 1470449587
Category : Mathematics
Languages : en
Pages : 100
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Author: Gijs Heuts
Publisher: American Mathematical Society
ISBN: 1470448939
Category : Mathematics
Languages : en
Pages : 108
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