The Creation Of Strange Non Chaotic Attractors In Non Smooth Saddle Node Bifurcations
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The Creation Of Strange Non Chaotic Attractors In Non Smooth Saddle Node Bifurcations
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Author : Tobias H. Jger
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-08-07
The Creation Of Strange Non Chaotic Attractors In Non Smooth Saddle Node Bifurcations written by Tobias H. Jger and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-07 with Mathematics categories.
The author proposes a general mechanism by which strange non-chaotic attractors (SNA) are created during the collision of invariant curves in quasiperiodically forced systems. This mechanism, and its implementation in different models, is first discussed on an heuristic level and by means of simulations. In the considered examples, a stable and an unstable invariant circle undergo a saddle-node bifurcation, but instead of a neutral invariant curve there exists a strange non-chaotic attractor-repeller pair at the bifurcation point. This process is accompanied by a very characteristic behaviour of the invariant curves prior to their collision, which the author calls `exponential evolution of peaks'.
Strange Nonchaotic Attractors
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Author : Ulrike Feudel
language : en
Publisher: World Scientific
Release Date : 2006
Strange Nonchaotic Attractors written by Ulrike Feudel and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Science categories.
This book is the first monograph devoted exclusively to strange nonchaotic attractors (SNA), recently discovered objects with a special kind of dynamical behavior between order and chaos in dissipative nonlinear systems under quasiperiodic driving. A historical review of the discovery and study of SNA, mathematical and physically-motivated examples, and a review of known experimental studies of SNA are presented. The main focus is on the theoretical analysis of strange nonchaotic behavior by means of different tools of nonlinear dynamics and statistical physics (bifurcation analysis, Lyapunov exponents, correlations and spectra, renormalization group). The relations of the subject to other fields of physics such as quantum chaos and solid state physics are also discussed. Sample Chapter(s). Chapter 1: Introduction (122 KB). Contents: Models; Rational Approximations; Stability and Instability; Fractal and Statistical Properties; Bifurcations in Quasiperiodically Forced Systems and Transitions to SNA; Renormalization Group Approach to the Onset of SNA in Maps with the Golden-Mean Quasiperiodic Driving. Readership: Graduate students and researchers in nonlinear science.
Yang Mills Connections On Orientable And Nonorientable Surfaces
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Author : Nan-Kuo Ho
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-10-08
Yang Mills Connections On Orientable And Nonorientable Surfaces written by Nan-Kuo Ho and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-08 with Mathematics categories.
In ``The Yang-Mills equations over Riemann surfaces'', Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. In ``Yang-Mills Connections on Nonorientable Surfaces'', the authors study Yang-Mills functional on the space of connections on a principal $G_{\mathbb{R}}$-bundle over a closed, connected, nonorientable surface, where $G_{\mathbb{R}}$ is any compact connected Lie group. In this monograph, the authors generalize the discussion in ``The Yang-Mills equations over Riemann surfaces'' and ``Yang-Mills Connections on Nonorientable Surfaces''. They obtain explicit descriptions of equivariant Morse stratification of Yang-Mills functional on orientable and nonorientable surfaces for non-unitary classical groups $SO(n)$ and $Sp(n)$.
Unfolding Cr Singularities
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Author : Adam Coffman
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Unfolding Cr Singularities written by Adam Coffman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
"Volume 205, number 962 (first of 5 numbers)."
Invariant Representations Of Mathrm Gsp 2 Under Tensor Product With A Quadratic Character
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Author : Ping-Shun Chan
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Invariant Representations Of Mathrm Gsp 2 Under Tensor Product With A Quadratic Character written by Ping-Shun Chan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
"Volume 204, number 957 (first of 5 numbers)."
Two Kinds Of Derived Categories Koszul Duality And Comodule Contramodule Correspondence
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Author : Leonid Positselski
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Two Kinds Of Derived Categories Koszul Duality And Comodule Contramodule Correspondence written by Leonid Positselski and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
"July 2011, volume 212, number 996 (first of 4 numbers)."
C Algebras Of Homoclinic And Heteroclinic Structure In Expansive Dynamics
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Author : Klaus Thomsen
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-06-11
C Algebras Of Homoclinic And Heteroclinic Structure In Expansive Dynamics written by Klaus Thomsen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-11 with Mathematics categories.
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.
Lyapunov Exponents And Invariant Manifolds For Random Dynamical Systems In A Banach Space
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Author : Zeng Lian
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Lyapunov Exponents And Invariant Manifolds For Random Dynamical Systems In A Banach Space written by Zeng Lian and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
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.
Differential Forms On Wasserstein Space And Infinite Dimensional Hamiltonian Systems
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Author : Wilfrid Gangbo
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Differential Forms On Wasserstein Space And Infinite Dimensional Hamiltonian Systems written by Wilfrid Gangbo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Let $\mathcal{M}$ denote the space of probability measures on $\mathbb{R}^D$ endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely continuous curves in $\mathcal{M}$ was introduced by Ambrosio, Gigli, and Savare. In this paper the authors develop a calculus for the corresponding class of differential forms on $\mathcal{M}$. In particular they prove an analogue of Green's theorem for 1-forms and show that the corresponding first cohomology group, in the sense of de Rham, vanishes. For $D=2d$ the authors then define a symplectic distribution on $\mathcal{M}$ in terms of this calculus, thus obtaining a rigorous framework for the notion of Hamiltonian systems as introduced by Ambrosio and Gangbo. Throughout the paper the authors emphasize the geometric viewpoint and the role played by certain diffeomorphism groups of $\mathbb{R}^D$.
Small Modifications Of Quadrature Domains
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Author : Makoto Sakai
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Small Modifications Of Quadrature Domains written by Makoto Sakai and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
For a given plane domain, the author adds a constant multiple of the Dirac measure at a point in the domain and makes a new domain called a quadrature domain. The quadrature domain is characterized as a domain such that the integral of a harmonic and integrable function over the domain equals the integral of the function over the given domain plus the integral of the function with respect to the added measure. The family of quadrature domains can be modeled as the Hele-Shaw flow with a free-boundary problem. The given domain is regarded as the initial domain and the support point of the Dirac measure as the injection point of the flow.