The Maslov Index In Symplectic Banach Spaces

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The Maslov Index in Symplectic Banach Spaces

Author : Bernhelm Booß-Bavnbek
Publisher : American Mathematical Soc.
ISBN 13 : 1470428008
Total Pages : 123 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Maslov Index in Symplectic Banach Spaces by : Bernhelm Booß-Bavnbek

Download or read book The Maslov Index in Symplectic Banach Spaces written by Bernhelm Booß-Bavnbek and published by American Mathematical Soc.. This book was released on 2018-03-19 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying weak symplectic structures. Assuming vanishing index, they obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions the authors define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. The authors prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction while recovering all the standard properties of the Maslov index. As an application, the authors consider curves of elliptic operators which have varying principal symbol, varying maximal domain and are not necessarily of Dirac type. For this class of operator curves, the authors derive a desuspension spectral flow formula for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds.

The Maslov Index in Symplectic Banach Spaces

Author : Bernhelm Booss
Publisher :
ISBN 13 : 9781470443719
Total Pages : 118 pages
Book Rating : 4.4/5 (437 download)

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Book Synopsis The Maslov Index in Symplectic Banach Spaces by : Bernhelm Booss

Download or read book The Maslov Index in Symplectic Banach Spaces written by Bernhelm Booss and published by . This book was released on 2018 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Noncommutative Maslov Index and Eta-Forms

Author : Charlotte Wahl
Publisher : American Mathematical Soc.
ISBN 13 : 0821839977
Total Pages : 130 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Noncommutative Maslov Index and Eta-Forms by : Charlotte Wahl

Download or read book Noncommutative Maslov Index and Eta-Forms written by Charlotte Wahl and published by American Mathematical Soc.. This book was released on 2007 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author defines and proves a noncommutative generalization of a formula relating the Maslov index of a triple of Lagrangian subspaces of a symplectic vector space to eta-invariants associated to a pair of Lagrangian subspaces. The noncommutative Maslov index, defined for modules over a $C *$-algebra $\mathcal{A}$, is an element in $K_0(\mathcal{A})$. The generalized formula calculates its Chern character in the de Rham homology of certain dense subalgebras of $\mathcal{A}$. The proof is a noncommutative Atiyah-Patodi-Singer index theorem for a particular Dirac operator twisted by an $\mathcal{A}$-vector bundle. The author develops an analytic framework for this type of index problem.

On the Geometric Side of the Arthur Trace Formula for the Symplectic Group of Rank 2

Author : Werner Hoffmann
Publisher : American Mathematical Soc.
ISBN 13 : 1470431025
Total Pages : 88 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis On the Geometric Side of the Arthur Trace Formula for the Symplectic Group of Rank 2 by : Werner Hoffmann

Download or read book On the Geometric Side of the Arthur Trace Formula for the Symplectic Group of Rank 2 written by Werner Hoffmann and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the non-semisimple terms in the geometric side of the Arthur trace formula for the split symplectic similitude group and the split symplectic group of rank over any algebraic number field. In particular, they express the global coefficients of unipotent orbital integrals in terms of Dedekind zeta functions, Hecke -functions, and the Shintani zeta function for the space of binary quadratic forms.

Measure and Capacity of Wandering Domains in Gevrey Near-Integrable Exact Symplectic Systems

Author : Laurent Lazzarini
Publisher : American Mathematical Soc.
ISBN 13 : 147043492X
Total Pages : 106 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Measure and Capacity of Wandering Domains in Gevrey Near-Integrable Exact Symplectic Systems by : Laurent Lazzarini

Download or read book Measure and Capacity of Wandering Domains in Gevrey Near-Integrable Exact Symplectic Systems written by Laurent Lazzarini and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: A wandering domain for a diffeomorphism of is an open connected set such that for all . The authors endow with its usual exact symplectic structure. An integrable diffeomorphism, i.e., the time-one map of a Hamiltonian which depends only on the action variables, has no nonempty wandering domains. The aim of this paper is to estimate the size (measure and Gromov capacity) of wandering domains in the case of an exact symplectic perturbation of , in the analytic or Gevrey category. Upper estimates are related to Nekhoroshev theory; lower estimates are related to examples of Arnold diffusion. This is a contribution to the “quantitative Hamiltonian perturbation theory” initiated in previous works on the optimality of long term stability estimates and diffusion times; the emphasis here is on discrete systems because this is the natural setting to study wandering domains.

Elliptic PDEs on Compact Ricci Limit Spaces and Applications

Author : Shouhei Honda
Publisher : American Mathematical Soc.
ISBN 13 : 1470428547
Total Pages : 92 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Elliptic PDEs on Compact Ricci Limit Spaces and Applications by : Shouhei Honda

Download or read book Elliptic PDEs on Compact Ricci Limit Spaces and Applications written by Shouhei Honda and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the author studies elliptic PDEs on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds. In particular the author establishes continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schrödinger operators, generalized Yamabe constants and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology. The author applies these to the study of second-order differential calculus on such limit spaces.

Globally Generated Vector Bundles with Small C1 on Projective Spaces

Author : Cristian Anghel
Publisher : American Mathematical Soc.
ISBN 13 : 1470428385
Total Pages : 107 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Globally Generated Vector Bundles with Small C1 on Projective Spaces by : Cristian Anghel

Download or read book Globally Generated Vector Bundles with Small C1 on Projective Spaces written by Cristian Anghel and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spectral Flow

Author : Nora Doll
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111172473
Total Pages : 460 pages
Book Rating : 4.1/5 (111 download)

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Book Synopsis Spectral Flow by : Nora Doll

Download or read book Spectral Flow written by Nora Doll and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-06-19 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analytic Trends in Mathematical Physics

Author : Houssam Abdul-Rahman
Publisher : American Mathematical Soc.
ISBN 13 : 1470448416
Total Pages : 206 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Analytic Trends in Mathematical Physics by : Houssam Abdul-Rahman

Download or read book Analytic Trends in Mathematical Physics written by Houssam Abdul-Rahman and published by American Mathematical Soc.. This book was released on 2020-01-06 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Arizona School of Analysis and Mathematical Physics, held from March 5–9, 2018, at the University of Arizona, Tucson, Arizona. A main goal of this school was to introduce graduate students and postdocs to exciting topics of current research that are both influenced by physical intuition and require the use of cutting-edge mathematics. The articles in this volume reflect recent progress and innovative techniques developed within mathematical physics. Two works investigate spectral gaps of quantum spin systems. Specifically, Abdul-Rahman, Lemm, Lucia, Nachtergaele, and Young consider decorated AKLT models, and Lemm demonstrates a finite-size criterion for D D-dimensional models. Bachmann, De Roeck, and Fraas summarize a recent proof of the adiabatic theorem, while Bachmann, Bols, De Roeck, and Fraas discuss linear response for interacting Hall insulators. Models on general graphs are the topic of the articles by Fischbacher, on higher spin XXZ, and by Latushkin and Sukhtaiev, on an index theorem for Schrödinger operators. Probabilistic applications are the focus of the articles by DeMuse and Yin, on exponential random graphs, by Saenz, on KPZ universality, and by Stolz, on disordered quantum spin chains. In all, the diversity represented here is a testament to the enthusiasm this rich field of mathematical physics generates.

Diophantine Approximation and the Geometry of Limit Sets in Gromov Hyperbolic Metric Spaces

Author : Lior Fishman
Publisher : American Mathematical Soc.
ISBN 13 : 1470428865
Total Pages : 137 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Diophantine Approximation and the Geometry of Limit Sets in Gromov Hyperbolic Metric Spaces by : Lior Fishman

Download or read book Diophantine Approximation and the Geometry of Limit Sets in Gromov Hyperbolic Metric Spaces written by Lior Fishman and published by American Mathematical Soc.. This book was released on 2018-08-09 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the authors provide a complete theory of Diophantine approximation in the limit set of a group acting on a Gromov hyperbolic metric space. This summarizes and completes a long line of results by many authors, from Patterson's classic 1976 paper to more recent results of Hersonsky and Paulin (2002, 2004, 2007). The authors consider concrete examples of situations which have not been considered before. These include geometrically infinite Kleinian groups, geometrically finite Kleinian groups where the approximating point is not a fixed point of any element of the group, and groups acting on infinite-dimensional hyperbolic space. Moreover, in addition to providing much greater generality than any prior work of which the authors are aware, the results also give new insight into the nature of the connection between Diophantine approximation and the geometry of the limit set within which it takes place. Two results are also contained here which are purely geometric: a generalization of a theorem of Bishop and Jones (1997) to Gromov hyperbolic metric spaces, and a proof that the uniformly radial limit set of a group acting on a proper geodesic Gromov hyperbolic metric space has zero Patterson–Sullivan measure unless the group is quasiconvex-cocompact. The latter is an application of a Diophantine theorem.

Bellman Function for Extremal Problems in BMO II: Evolution

Author : Paata Ivanisvili
Publisher : American Mathematical Soc.
ISBN 13 : 1470429543
Total Pages : 136 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Bellman Function for Extremal Problems in BMO II: Evolution by : Paata Ivanisvili

Download or read book Bellman Function for Extremal Problems in BMO II: Evolution written by Paata Ivanisvili and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a previous study, the authors built the Bellman function for integral functionals on the space. The present paper provides a development of the subject. They abandon the majority of unwanted restrictions on the function that generates the functional. It is the new evolutional approach that allows the authors to treat the problem in its natural setting. What is more, these new considerations lighten dynamical aspects of the Bellman function, in particular, the evolution of its picture.

On Mesoscopic Equilibrium for Linear Statistics in Dyson’s Brownian Motion

Author : Maurice Duits
Publisher : American Mathematical Soc.
ISBN 13 : 1470429640
Total Pages : 118 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis On Mesoscopic Equilibrium for Linear Statistics in Dyson’s Brownian Motion by : Maurice Duits

Download or read book On Mesoscopic Equilibrium for Linear Statistics in Dyson’s Brownian Motion written by Maurice Duits and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors study mesoscopic fluctuations for Dyson's Brownian motion with β=2 . Dyson showed that the Gaussian Unitary Ensemble (GUE) is the invariant measure for this stochastic evolution and conjectured that, when starting from a generic configuration of initial points, the time that is needed for the GUE statistics to become dominant depends on the scale we look at: The microscopic correlations arrive at the equilibrium regime sooner than the macrosopic correlations. The authors investigate the transition on the intermediate, i.e. mesoscopic, scales. The time scales that they consider are such that the system is already in microscopic equilibrium (sine-universality for the local correlations), but have not yet reached equilibrium at the macrosopic scale. The authors describe the transition to equilibrium on all mesoscopic scales by means of Central Limit Theorems for linear statistics with sufficiently smooth test functions. They consider two situations: deterministic initial points and randomly chosen initial points. In the random situation, they obtain a transition from the classical Central Limit Theorem for independent random variables to the one for the GUE.

Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations

Author : T. Alazard
Publisher : American Mathematical Soc.
ISBN 13 : 147043203X
Total Pages : 108 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations by : T. Alazard

Download or read book Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations written by T. Alazard and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves, the authors consider solutions such that the curvature of the initial free surface does not belong to L2. The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Hölder estimates. The authors first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then use the dispersive properties of the water-waves system, namely Strichartz estimates, to control these Hölder norms.

Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths

Author : Sergey Fomin
Publisher : American Mathematical Soc.
ISBN 13 : 1470429675
Total Pages : 98 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths by : Sergey Fomin

Download or read book Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths written by Sergey Fomin and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, the authors construct a geometric realization in terms of suitable decorated Teichmüller space of the surface. On the geometric side, this requires opening the surface at each interior marked point into an additional geodesic boundary component. On the algebraic side, it relies on the notion of a non-normalized cluster algebra and the machinery of tropical lambda lengths. The authors' model allows for an arbitrary choice of coefficients which translates into a choice of a family of integral laminations on the surface. It provides an intrinsic interpretation of cluster variables as renormalized lambda lengths of arcs on the surface. Exchange relations are written in terms of the shear coordinates of the laminations and are interpreted as generalized Ptolemy relations for lambda lengths. This approach gives alternative proofs for the main structural results from the authors' previous paper, removing unnecessary assumptions on the surface.

Algebraic Q-Groups as Abstract Groups

Author : Olivier Frécon
Publisher : American Mathematical Soc.
ISBN 13 : 1470429233
Total Pages : 99 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebraic Q-Groups as Abstract Groups by : Olivier Frécon

Download or read book Algebraic Q-Groups as Abstract Groups written by Olivier Frécon and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author analyzes the abstract structure of algebraic groups over an algebraically closed field . For of characteristic zero and a given connected affine algebraic Q -group, the main theorem describes all the affine algebraic Q -groups such that the groups and are isomorphic as abstract groups. In the same time, it is shown that for any two connected algebraic Q -groups and , the elementary equivalence of the pure groups and implies that they are abstractly isomorphic. In the final section, the author applies his results to characterize the connected algebraic groups, all of whose abstract automorphisms are standard, when is either Q or of positive characteristic. In characteristic zero, a fairly general criterion is exhibited.

Perihelia Reduction and Global Kolmogorov Tori in the Planetary Problem

Author : Gabriella Pinzari
Publisher : American Mathematical Soc.
ISBN 13 : 1470441020
Total Pages : 92 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Perihelia Reduction and Global Kolmogorov Tori in the Planetary Problem by : Gabriella Pinzari

Download or read book Perihelia Reduction and Global Kolmogorov Tori in the Planetary Problem written by Gabriella Pinzari and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author proves the existence of an almost full measure set of -dimensional quasi-periodic motions in the planetary problem with masses, with eccentricities arbitrarily close to the Levi–Civita limiting value and relatively high inclinations. This extends previous results, where smallness of eccentricities and inclinations was assumed. The question had been previously considered by V. I. Arnold in the 1960s, for the particular case of the planar three-body problem, where, due to the limited number of degrees of freedom, it was enough to use the invariance of the system by the SO(3) group. The proof exploits nice parity properties of a new set of coordinates for the planetary problem, which reduces completely the number of degrees of freedom for the system (in particular, its degeneracy due to rotations) and, moreover, is well fitted to its reflection invariance. It allows the explicit construction of an associated close to be integrable system, replacing Birkhoff normal form, a common tool of previous literature.

Global Regularity for 2D Water Waves with Surface Tension

Author : Alexandru D. Ionescu
Publisher : American Mathematical Soc.
ISBN 13 : 1470431033
Total Pages : 123 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Global Regularity for 2D Water Waves with Surface Tension by : Alexandru D. Ionescu

Download or read book Global Regularity for 2D Water Waves with Surface Tension written by Alexandru D. Ionescu and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An important point of the authors' analysis is to develop a sufficiently robust method (the “quasilinear I-method”) which allows the authors to deal with strong singularities arising from time resonances in the applications of the normal form method (the so-called “division problem”). As a result, they are able to consider a suitable class of perturbations with finite energy, but no other momentum conditions. Part of the authors' analysis relies on a new treatment of the Dirichlet-Neumann operator in dimension two which is of independent interest. As a consequence, the results in this paper are self-contained.