Multi Pulse Evolution And Space Time Chaos In Dissipative Systems

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Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems

Sergey Zelik,Alexander Mielke
Multi Pulse Evolution and Space Time Chaos in Dissipative Systems Book PDF

Author : Sergey Zelik,Alexander Mielke
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 43,7 Mb
Release : 2009-03-06
Category : Mathematics
ISBN : 9780821842645

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Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems by Sergey Zelik,Alexander Mielke Pdf

The authors study semilinear parabolic systems on the full space ${\mathbb R}^n$ that admit a family of exponentially decaying pulse-like steady states obtained via translations. The multi-pulse solutions under consideration look like the sum of infinitely many such pulses which are well separated. They prove a global center-manifold reduction theorem for the temporal evolution of such multi-pulse solutions and show that the dynamics of these solutions can be described by an infinite system of ODEs for the positions of the pulses. As an application of the developed theory, The authors verify the existence of Sinai-Bunimovich space-time chaos in 1D space-time periodically forced Swift-Hohenberg equation.

The Creation of Strange Non-Chaotic Attractors in Non-Smooth Saddle-Node Bifurcations

Tobias H. JŠger
The Creation of Strange Non Chaotic Attractors in Non Smooth Saddle Node Bifurcations Book PDF

Author : Tobias H. JŠger
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 43,5 Mb
Release : 2009-08-07
Category : Mathematics
ISBN : 9780821844274

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The Creation of Strange Non-Chaotic Attractors in Non-Smooth Saddle-Node Bifurcations by Tobias H. JŠger Pdf

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'.

Scattering Resonances for Several Small Convex Bodies and the Lax-Phillips Conjecture

Luchezar N. Stoyanov
Scattering Resonances for Several Small Convex Bodies and the Lax Phillips Conjecture Book PDF

Author : Luchezar N. Stoyanov
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 51,7 Mb
Release : 2009
Category : Algebraic spaces
ISBN : 9780821842942

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Scattering Resonances for Several Small Convex Bodies and the Lax-Phillips Conjecture by Luchezar N. Stoyanov Pdf

This work deals with scattering by obstacles which are finite disjoint unions of strictly convex bodies with smooth boundaries in an odd dimensional Euclidean space. The class of obstacles of this type which is considered are contained in a given (large) ball and have some additional properties.

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

Zeng Lian,Kening Lu
Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space Book PDF

Author : Zeng Lian,Kening Lu
Publisher : American Mathematical Soc.
Page : 119 pages
File Size : 42,7 Mb
Release : 2010
Category : Banach spaces
ISBN : 9780821846568

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Lyapunov Exponents and Invariant Manifolds for Random Dynamical Systems in a Banach Space by Zeng Lian,Kening Lu Pdf

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.

Random Sets and Invariants for (Type II) Continuous Tensor Product Systems of Hilbert Spaces

Volkmar Liebscher
Random Sets and Invariants for Type II Continuous Tensor Product Systems of Hilbert Spaces Book PDF

Author : Volkmar Liebscher
Publisher : American Mathematical Soc.
Page : 124 pages
File Size : 46,5 Mb
Release : 2009-04-10
Category : Mathematics
ISBN : 9780821843185

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Random Sets and Invariants for (Type II) Continuous Tensor Product Systems of Hilbert Spaces by Volkmar Liebscher Pdf

In a series of papers Tsirelson constructed from measure types of random sets or (generalised) random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying $E_0$-semigroups upto cocycle conjugacy. This paper starts from establishing the converse. So the author connects each continuous tensor product system of Hilbert spaces with measure types of distributions of random (closed) sets in $[0,1]$ or $\mathbb R_+$. These measure types are stationary and factorise over disjoint intervals. In a special case of this construction, the corresponding measure type is an invariant of the product system. This shows, completing in a more systematic way the Tsirelson examples, that the classification scheme for product systems into types $\mathrm{I}_n$, $\mathrm{II}_n$ and $\mathrm{III}$ is not complete. Moreover, based on a detailed study of this kind of measure types, the author constructs for each stationary factorising measure type a continuous tensor product system of Hilbert spaces such that this measure type arises as the before mentioned invariant.

Mixed-Norm Inequalities and Operator Space $L_p$ Embedding Theory

Marius Junge,Javier Parcet
Mixed Norm Inequalities and Operator Space L p Embedding Theory Book PDF

Author : Marius Junge,Javier Parcet
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 42,9 Mb
Release : 2010
Category : Banach spaces
ISBN : 9780821846551

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Mixed-Norm Inequalities and Operator Space $L_p$ Embedding Theory by Marius Junge,Javier Parcet Pdf

Contains the proof of a noncommutative analogue of the inequality for sums of free random variables over a given von Neumann subalgebra.

Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules

AndrŽ Martinez,Vania Sordoni
Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules Book PDF

Author : AndrŽ Martinez,Vania Sordoni
Publisher : American Mathematical Soc.
Page : 96 pages
File Size : 46,5 Mb
Release : 2009-06-05
Category : Mathematics
ISBN : 9780821842966

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Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules by AndrŽ Martinez,Vania Sordoni Pdf

The authors construct an abstract pseudodifferential calculus with operator-valued symbol, suitable for the treatment of Coulomb-type interactions, and they apply it to the study of the quantum evolution of molecules in the Born-Oppenheimer approximation, in the case of the electronic Hamiltonian admitting a local gap in its spectrum. In particular, they show that the molecular evolution can be reduced to the one of a system of smooth semiclassical operators, the symbol of which can be computed explicitely. In addition, they study the propagation of certain wave packets up to long time values of Ehrenfest order.

Approximate Homotopy of Homomorphisms from C(X) Into a Simple C*-algebra

Huaxin Lin
Approximate Homotopy of Homomorphisms from C X Into a Simple C algebra Book PDF

Author : Huaxin Lin
Publisher : American Mathematical Soc.
Page : 131 pages
File Size : 48,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821851944

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Approximate Homotopy of Homomorphisms from C(X) Into a Simple C*-algebra by Huaxin Lin Pdf

In this paper the author proves Generalized Homotopy Lemmas. These type of results play an important role in the classification theory of $*$-homomorphisms up to asymptotic unitary equivalence. Table of Contents: Prelude; The basic homotopy lemma for higher dimensional spaces; Purely infinite simple $C^*$-algebras; Approximate homotopy; Super homotopy; Postlude; Bibliography. (MEMO/205/963)

Unfolding CR Singularities

Adam Coffman
Unfolding CR Singularities Book PDF

Author : Adam Coffman
Publisher : American Mathematical Soc.
Page : 105 pages
File Size : 44,7 Mb
Release : 2010
Category : CR submanifolds
ISBN : 9780821846575

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Unfolding CR Singularities by Adam Coffman Pdf

"Volume 205, number 962 (first of 5 numbers)."

On a Conjecture of E. M. Stein on the Hilbert Transform on Vector Fields

Michael Thoreau Lacey,Xiaochun Li
On a Conjecture of E M Stein on the Hilbert Transform on Vector Fields Book PDF

Author : Michael Thoreau Lacey,Xiaochun Li
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 55,9 Mb
Release : 2010
Category : Harmonic analysis
ISBN : 9780821845400

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On a Conjecture of E. M. Stein on the Hilbert Transform on Vector Fields by Michael Thoreau Lacey,Xiaochun Li Pdf

"Volume 205, number 965 (fourth of 5 numbers)."

Operator Theory on Noncommutative Domains

Gelu Popescu
Operator Theory on Noncommutative Domains Book PDF

Author : Gelu Popescu
Publisher : American Mathematical Soc.
Page : 137 pages
File Size : 52,6 Mb
Release : 2010
Category : Dilation theory (Operator theory).
ISBN : 9780821847107

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Operator Theory on Noncommutative Domains by Gelu Popescu Pdf

"Volume 205, number 964 (third of 5 numbers)."

Banach Algebras on Semigroups and on Their Compactifications

Harold G. Dales,Anthony To-Ming Lau,Dona Strauss
Banach Algebras on Semigroups and on Their Compactifications Book PDF

Author : Harold G. Dales,Anthony To-Ming Lau,Dona Strauss
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 55,7 Mb
Release : 2010
Category : Banach algebras
ISBN : 9780821847756

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Banach Algebras on Semigroups and on Their Compactifications by Harold G. Dales,Anthony To-Ming Lau,Dona Strauss Pdf

"Volume 205, number 966 (end of volume)."

On the convergence of $\sum c_kf(n_kx)$

Istvan Berkes,Michel Weber
On the convergence of sum c kf n kx Book PDF

Author : Istvan Berkes,Michel Weber
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 46,8 Mb
Release : 2009
Category : Convergence
ISBN : 9780821843246

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On the convergence of $\sum c_kf(n_kx)$ by Istvan Berkes,Michel Weber Pdf

Presents a general study of the convergence problem and intends to prove several fresh results and improve a number of old results in the field. This title studies the case when the nk are random and investigates the discrepancy the sequence (nkx) mod 1.

Affine Insertion and Pieri Rules for the Affine Grassmannian

Thomas Lam
Affine Insertion and Pieri Rules for the Affine Grassmannian Book PDF

Author : Thomas Lam
Publisher : American Mathematical Soc.
Page : 82 pages
File Size : 55,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821846582

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Affine Insertion and Pieri Rules for the Affine Grassmannian by Thomas Lam Pdf

The authors study combinatorial aspects of the Schubert calculus of the affine Grassmannian ${\rm Gr}$ associated with $SL(n,\mathbb{C})$.Their main results are: Pieri rules for the Schubert bases of $H^*({\rm Gr})$ and $H_*({\rm Gr})$, which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. A new combinatorial definition for $k$-Schur functions, which represent the Schubert basis of $H_*({\rm Gr})$. A combinatorial interpretation of the pairing $H^*({\rm Gr})\times H_*({\rm Gr}) \rightarrow\mathbb Z$ induced by the cap product.

Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups

Drew Armstrong
Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups Book PDF

Author : Drew Armstrong
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 46,8 Mb
Release : 2009-10-08
Category : Mathematics
ISBN : 9780821844908

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Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups by Drew Armstrong Pdf

This memoir is a refinement of the author's PhD thesis -- written at Cornell University (2006). It is primarily a desription of new research but also includes a substantial amount of background material. At the heart of the memoir the author introduces and studies a poset $NC^{(k)}(W)$ for each finite Coxeter group $W$ and each positive integer $k$. When $k=1$, his definition coincides with the generalized noncrossing partitions introduced by Brady and Watt in $K(\pi, 1)$'s for Artin groups of finite type and Bessis in The dual braid monoid. When $W$ is the symmetric group, the author obtains the poset of classical $k$-divisible noncrossing partitions, first studied by Edelman in Chain enumeration and non-crossing partitions.