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 Business & Economics 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. Key Features Topics are suitable for various disciplines dealing with nonlinear dynamics (mechanics, physics, nonlinear optics, hydrodynamics, chemical kinetics, etc.) A variety of theoretical tools is supplied to reveal different characteristics of strange nonchaotic behavior Readership: Graduate students and researchers in nonlinear science.
Strange Nonchaotic Attractors
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language : en
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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.
The Parameterization Method For Invariant Manifolds
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Author : Àlex Haro
language : en
Publisher: Springer
Release Date : 2016-04-18
The Parameterization Method For Invariant Manifolds written by Àlex Haro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-18 with Mathematics categories.
This monograph presents some theoretical and computational aspects of the parameterization method for invariant manifolds, focusing on the following contexts: invariant manifolds associated with fixed points, invariant tori in quasi-periodically forced systems, invariant tori in Hamiltonian systems and normally hyperbolic invariant manifolds. This book provides algorithms of computation and some practical details of their implementation. The methodology is illustrated with 12 detailed examples, many of them well known in the literature of numerical computation in dynamical systems. A public version of the software used for some of the examples is available online. The book is aimed at mathematicians, scientists and engineers interested in the theory and applications of computational dynamical systems.
Center Manifolds For Semilinear Equations With Non Dense Domain And Applications To Hopf Bifurcation In Age Structured Models
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Author : Pierre Magal
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Center Manifolds For Semilinear Equations With Non Dense Domain And Applications To Hopf Bifurcation In Age Structured Models written by Pierre Magal 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 with Bifurcation theory categories.
Several types of differential equations, such as delay differential equations, age-structure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with non-dense domain. Using Liapunov-Perron method and following the techniques of Vanderbauwhede et al. in treating infinite dimensional systems, the authors study the existence and smoothness of center manifolds for semilinear Cauchy problems with non-dense domain. As an application, they use the center manifold theorem to establish a Hopf bifurcation theorem for age structured models.
Non Divergence Equations Structured On Hormander Vector Fields Heat Kernels And Harnack Inequalities
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Author : Marco Bramanti
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Non Divergence Equations Structured On Hormander Vector Fields Heat Kernels And Harnack Inequalities written by Marco Bramanti 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 Differential inequalities categories.
"March 2010, Volume 204, number 961 (end of volume)."
The Internally 4 Connected Binary Matroids With No M K 3 3 Minor
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Author : Dillon Mayhew
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
The Internally 4 Connected Binary Matroids With No M K 3 3 Minor written by Dillon Mayhew 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 Combinatorial designs and configurations categories.
The authors give a characterization of the internally $4$-connected binary matroids that have no minor isomorphic to $M(K_{3,3})$. Any such matroid is either cographic, or is isomorphic to a particular single-element extension of the bond matroid of a cubic or quartic Mobius ladder, or is isomorphic to one of eighteen sporadic matroids.
Classification Of Radial Solutions Arising In The Study Of Thermal Structures With Thermal Equilibrium Or No Flux At The Boundary
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Author : Alfonso Castro
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
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 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 Differential equations, Elliptic categories.
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.
Affine Insertion And Pieri Rules For The Affine Grassmannian
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Author : Thomas Lam
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Affine Insertion And Pieri Rules For The Affine Grassmannian written by Thomas Lam 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 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.