C Algebras Of Homoclinic And Heteroclinic Structure In Expansive Dynamics

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$C^*$-Algebras of Homoclinic and Heteroclinic Structure in Expansive Dynamics

Author : Klaus Thomsen
Publisher : American Mathematical Soc.
ISBN 13 : 0821846922
Total Pages : 138 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis $C^*$-Algebras of Homoclinic and Heteroclinic Structure in Expansive Dynamics by : Klaus Thomsen

Download or read book $C^*$-Algebras of Homoclinic and Heteroclinic Structure in Expansive Dynamics written by Klaus Thomsen and published by American Mathematical Soc.. This book was released on 2010-06-11 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author unifies various constructions of $C^*$-algebras from dynamical systems, specifically, the dimension group construction of Krieger for shift spaces, the corresponding constructions of Wagoner and Boyle, Fiebig and Fiebig for countable state Markov shifts and one-sided shift spaces, respectively, and the constructions of Ruelle and Putnam for Smale spaces. The general setup is used to analyze the structure of the $C^*$-algebras arising from the homoclinic and heteroclinic equivalence relations in expansive dynamical systems, in particular, expansive group endomorphisms and automorphisms and generalized 1-solenoids. For these dynamical systems it is shown that the $C^*$-algebras are inductive limits of homogeneous or sub-homogeneous algebras with one-dimensional spectra.

Operator Algebras for Multivariable Dynamics

Author : Kenneth R. Davidson
Publisher : American Mathematical Soc.
ISBN 13 : 0821853023
Total Pages : 68 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Operator Algebras for Multivariable Dynamics by : Kenneth R. Davidson

Download or read book Operator Algebras for Multivariable Dynamics written by Kenneth R. Davidson and published by American Mathematical Soc.. This book was released on 2011 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\sigma_i:X \to X$ for $1 \le i \le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\mathcal{A}(X,\tau)$ and the semicrossed product $\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.|Let $X$ be a locally compact Hausdorff space with $n$ proper continuous self maps $\sigma_i:X \to X$ for $1 \le i \le n$. To this the authors associate two conjugacy operator algebras which emerge as the natural candidates for the universal algebra of the system, the tensor algebra $\mathcal{A}(X,\tau)$ and the semicrossed product $\mathrm{C}_0(X)\times_\tau\mathbb{F}_n^+$. They develop the necessary dilation theory for both models. In particular, they exhibit an explicit family of boundary representations which determine the C*-envelope of the tensor algebra.

Modeling, Dynamics, Optimization and Bioeconomics IV

Author : Alberto Pinto
Publisher : Springer Nature
ISBN 13 : 3030781631
Total Pages : 448 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Modeling, Dynamics, Optimization and Bioeconomics IV by : Alberto Pinto

Download or read book Modeling, Dynamics, Optimization and Bioeconomics IV written by Alberto Pinto and published by Springer Nature. This book was released on 2021-09-29 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, following the three published volumes of the book, provides the main purpose to collect research papers and review papers to provide an overview of the main issues, results, and open questions in the cutting-edge research on the fields of modeling, optimization, and dynamics and their applications to biology, economy, energy, industry, physics, psychology and finance. Assuming the scientific relevance of the presenting innovative applications as well as merging issues in these areas, the purpose of this book is to collect papers of the world experts in mathematics, economics, and other applied sciences that is seminal to the future research developments. The majority of the papers presented in this book is authored by the participants in The Joint Meeting 6th International Conference on Dynamics, Games, and Science – DGSVI – JOLATE and in the 21st ICABR Conference. The scientific scope of the conferences is focused on the fields of modeling, optimization, and dynamics and their applications to biology, economy, energy, industry, physics, psychology, and finance. Assuming the scientific relevance of the presenting innovative applications as well as merging issues in these areas, the purpose of the conference is to bring together some of the world experts in mathematics, economics, and other applied sciences that reinforce ongoing projects and establish future works and collaborations.

Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space

Author : Zeng Lian
Publisher : American Mathematical Soc.
ISBN 13 : 0821846566
Total Pages : 119 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space by : Zeng Lian

Download or read book Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space written by Zeng Lian and published by American Mathematical Soc.. This book was released on 2010 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. The authors prove a multiplicative ergodic theorem and then use this theorem to establish the stable and unstable manifold theorem for nonuniformly hyperbolic random invariant sets.

Classification of Radial Solutions Arising in the Study of Thermal Structures with Thermal Equilibrium or No Flux at the Boundary

Author : Alfonso Castro
Publisher : American Mathematical Soc.
ISBN 13 : 0821847260
Total Pages : 87 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Classification of Radial Solutions Arising in the Study of Thermal Structures with Thermal Equilibrium or No Flux at the Boundary by : Alfonso Castro

Download or read book Classification of Radial Solutions Arising in the Study of Thermal Structures with Thermal Equilibrium or No Flux at the Boundary written by Alfonso Castro and published by American Mathematical Soc.. This book was released on 2010 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors provide a complete classification of the radial solutions to a class of reaction diffusion equations arising in the study of thermal structures such as plasmas with thermal equilibrium or no flux at the boundary. In particular, their study includes rapidly growing nonlinearities, that is, those where an exponent exceeds the critical exponent. They describe the corresponding bifurcation diagrams and determine existence and uniqueness of ground states, which play a central role in characterizing those diagrams. They also provide information on the stability-unstability of the radial steady states.

Dimer Models and Calabi-Yau Algebras

Author : Nathan Broomhead
Publisher : American Mathematical Soc.
ISBN 13 : 0821853082
Total Pages : 101 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Dimer Models and Calabi-Yau Algebras by : Nathan Broomhead

Download or read book Dimer Models and Calabi-Yau Algebras written by Nathan Broomhead and published by American Mathematical Soc.. This book was released on 2012-01-23 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article the author uses techniques from algebraic geometry and homological algebra, together with ideas from string theory to construct a class of 3-dimensional Calabi-Yau algebras. The Calabi-Yau property appears throughout geometry and string theory and is increasingly being studied in algebra. He further shows that the algebras constructed are examples of non-commutative crepant resolutions (NCCRs), in the sense of Van den Bergh, of Gorenstein affine toric threefolds. Dimer models, first studied in theoretical physics, give a way of writing down a class of non-commutative algebras, as the path algebra of a quiver with relations obtained from a `superpotential'. Some examples are Calabi-Yau and some are not. The author considers two types of `consistency' conditions on dimer models, and shows that a `geometrically consistent' dimer model is `algebraically consistent'. He proves that the algebras obtained from algebraically consistent dimer models are 3-dimensional Calabi-Yau algebras. This is the key step which allows him to prove that these algebras are NCCRs of the Gorenstein affine toric threefolds associated to the dimer models.

A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations

Author : Greg Kuperberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821853414
Total Pages : 153 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations by : Greg Kuperberg

Download or read book A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations written by Greg Kuperberg and published by American Mathematical Soc.. This book was released on 2012 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: In A von Neumann Algebra Approach to Quantum Metrics, Kuperberg and Weaver propose a new definition of quantum metric spaces, or W*-metric spaces, in the setting of von Neumann algebras. Their definition effectively reduces to the classical notion in the atomic abelian case, has both concrete and intrinsic characterizations, and admits a wide variety of tractable examples. A natural application and motivation of their theory is a mutual generalization of the standard models of classical and quantum error correction. In Quantum Relations Weaver defines a ``quantum relation'' on a von Neumann algebra $\mathcal{M}\subseteq\mathcal{B}(H)$ to be a weak* closed operator bimodule over its commutant $\mathcal{M}'$. Although this definition is framed in terms of a particular representation of $\mathcal{M}$, it is effectively representation independent. Quantum relations on $l^\infty(X)$ exactly correspond to subsets of $X^2$, i.e., relations on $X$. There is also a good definition of a ``measurable relation'' on a measure space, to which quantum relations partially reduce in the general abelian case. By analogy with the classical setting, Weaver can identify structures such as quantum equivalence relations, quantum partial orders, and quantum graphs, and he can generalize Arveson's fundamental work on weak* closed operator algebras containing a masa to these cases. He is also able to intrinsically characterize the quantum relations on $\mathcal{M}$ in terms of families of projections in $\mathcal{M}{\overline{\otimes}} \mathcal{B}(l^2)$.

The Generalized Fitting Subsystem of a Fusion System

Author : Michael Aschbacher
Publisher : American Mathematical Soc.
ISBN 13 : 0821853031
Total Pages : 122 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Generalized Fitting Subsystem of a Fusion System by : Michael Aschbacher

Download or read book The Generalized Fitting Subsystem of a Fusion System written by Michael Aschbacher and published by American Mathematical Soc.. This book was released on 2011-01-20 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, the author seeks to build a local theory of fusion systems, analogous to the local theory of finite groups, involving normal subsystems and factor systems.

Towards Non-Abelian P-adic Hodge Theory in the Good Reduction Case

Author : Martin C. Olsson
Publisher : American Mathematical Soc.
ISBN 13 : 082185240X
Total Pages : 170 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Towards Non-Abelian P-adic Hodge Theory in the Good Reduction Case by : Martin C. Olsson

Download or read book Towards Non-Abelian P-adic Hodge Theory in the Good Reduction Case written by Martin C. Olsson and published by American Mathematical Soc.. This book was released on 2011-02-07 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops a non-abelian version of $p$-adic Hodge Theory for varieties (possibly open with ``nice compactification'') with good reduction. This theory yields in particular a comparison between smooth $p$-adic sheaves and $F$-isocrystals on the level of certain Tannakian categories, $p$-adic Hodge theory for relative Malcev completions of fundamental groups and their Lie algebras, and gives information about the action of Galois on fundamental groups.

The Hermitian Two Matrix Model with an Even Quartic Potential

Author : Maurice Duits
Publisher : American Mathematical Soc.
ISBN 13 : 0821869280
Total Pages : 118 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Hermitian Two Matrix Model with an Even Quartic Potential by : Maurice Duits

Download or read book The Hermitian Two Matrix Model with an Even Quartic Potential written by Maurice Duits and published by American Mathematical Soc.. This book was released on 2012 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the two matrix model with an even quartic potential $W(y)=y^4/4+\alpha y^2/2$ and an even polynomial potential $V(x)$. The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices $M_1$. The vector equilibrium problem is defined for three measures, with external fields on the first and third measures and an upper constraint on the second measure. The proof is based on a steepest descent analysis of a $4\times4$ matrix valued Riemann-Hilbert problem that characterizes the correlation kernel for the eigenvalues of $M_1$. The authors' results generalize earlier results for the case $\alpha=0$, where the external field on the third measure was not present.

Networking Seifert Surgeries on Knots

Author : Arnaud Deruelle
Publisher : American Mathematical Soc.
ISBN 13 : 0821853333
Total Pages : 145 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Networking Seifert Surgeries on Knots by : Arnaud Deruelle

Download or read book Networking Seifert Surgeries on Knots written by Arnaud Deruelle and published by American Mathematical Soc.. This book was released on 2012 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors propose a new approach in studying Dehn surgeries on knots in the $3$-sphere $S^3$ yielding Seifert fiber spaces. The basic idea is finding relationships among such surgeries. To describe relationships and get a global picture of Seifert surgeries, they introduce ``seiferters'' and the Seifert Surgery Network, a $1$-dimensional complex whose vertices correspond to Seifert surgeries. A seiferter for a Seifert surgery on a knot $K$ is a trivial knot in $S^3$ disjoint from $K$ that becomes a fiber in the resulting Seifert fiber space. Twisting $K$ along its seiferter or an annulus cobounded by a pair of its seiferters yields another knot admitting a Seifert surgery. Edges of the network correspond to such twistings. A path in the network from one Seifert surgery to another explains how the former Seifert surgery is obtained from the latter after a sequence of twistings along seiferters and/or annuli cobounded by pairs of seiferters. The authors find explicit paths from various known Seifert surgeries to those on torus knots, the most basic Seifert surgeries. The authors classify seiferters and obtain some fundamental results on the structure of the Seifert Surgery Network. From the networking viewpoint, they find an infinite family of Seifert surgeries on hyperbolic knots which cannot be embedded in a genus two Heegaard surface of $S^3$.

Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

Author : Ross Lawther
Publisher : American Mathematical Soc.
ISBN 13 : 0821847694
Total Pages : 201 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups by : Ross Lawther

Download or read book Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups written by Ross Lawther and published by American Mathematical Soc.. This book was released on 2011 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let G be a simple algebraic group defined over an algebraically closed field k whose characteristic is either 0 or a good prime for G, and let uEG be unipotent. The authors study the centralizer CG(u), especially its centre Z(CG(u)). They calculate the Lie algebra of Z(CG(u)), in particular determining its dimension; they prove a succession of theorems of increasing generality, the last of which provides a formula for dim Z(CG(u)) in terms of the labelled diagram associated to the conjugacy class containing u.

Definable Additive Categories: Purity and Model Theory

Author : Mike Prest
Publisher : American Mathematical Soc.
ISBN 13 : 0821847678
Total Pages : 122 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Definable Additive Categories: Purity and Model Theory by : Mike Prest

Download or read book Definable Additive Categories: Purity and Model Theory written by Mike Prest and published by American Mathematical Soc.. This book was released on 2011-02-07 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of the model theory of modules works, with only minor modifications, in much more general additive contexts (such as functor categories, categories of comodules, categories of sheaves). Furthermore, even within a given category of modules, many subcategories form a ``self-sufficient'' context in which the model theory may be developed without reference to the larger category of modules. The notion of a definable additive category covers all these contexts. The (imaginaries) language which one uses for model theory in a definable additive category can be obtained from the category (of structures and homomorphisms) itself, namely, as the category of those functors to the category of abelian groups which commute with products and direct limits. Dually, the objects of the definable category--the modules (or functors, or comodules, or sheaves)--to which that model theory applies may be recovered as the exact functors from the, small abelian, category (the category of pp-imaginaries) which underlies that language.

On First and Second Order Planar Elliptic Equations with Degeneracies

Author : Abdelhamid Meziani
Publisher : American Mathematical Soc.
ISBN 13 : 0821853120
Total Pages : 90 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On First and Second Order Planar Elliptic Equations with Degeneracies by : Abdelhamid Meziani

Download or read book On First and Second Order Planar Elliptic Equations with Degeneracies written by Abdelhamid Meziani and published by American Mathematical Soc.. This book was released on 2012 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed. Properties of solutions, in a neighborhood of the degeneracy curve, are obtained through integral and series representations. An application to a second order elliptic equation with a punctual singularity is given.

Robin Functions for Complex Manifolds and Applications

Author : Kang-Tae Kim
Publisher : American Mathematical Soc.
ISBN 13 : 0821849654
Total Pages : 126 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Robin Functions for Complex Manifolds and Applications by : Kang-Tae Kim

Download or read book Robin Functions for Complex Manifolds and Applications written by Kang-Tae Kim and published by American Mathematical Soc.. This book was released on 2011 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 209, number 984 (third of 5 numbers)."

The Moduli Space of Cubic Threefolds as a Ball Quotient

Author : Daniel Allcock
Publisher : American Mathematical Soc.
ISBN 13 : 0821847511
Total Pages : 89 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Moduli Space of Cubic Threefolds as a Ball Quotient by : Daniel Allcock

Download or read book The Moduli Space of Cubic Threefolds as a Ball Quotient written by Daniel Allcock and published by American Mathematical Soc.. This book was released on 2011 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 209, number 985 (fourth of 5 numbers)."

Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part I

Author : Mark P. Walsh
Publisher : American Mathematical Soc.
ISBN 13 : 082185304X
Total Pages : 105 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part I by : Mark P. Walsh

Download or read book Metrics of Positive Scalar Curvature and Generalised Morse Functions, Part I written by Mark P. Walsh and published by American Mathematical Soc.. This book was released on 2011 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that isotopic metrics of positive scalar curvature are concordant. Whether or not the converse holds is an open question, at least in dimensions greater than four. The author shows that for a particular type of concordance, constructed using the surgery techniques of Gromov and Lawson, this converse holds in the case of closed simply connected manifolds of dimension at least five.