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Dimensions, Embeddings, and Attractors

Author : James C. Robinson

Publisher : Cambridge University Press

Page : 219 pages

File Size : 44,59 MB

Release : 2010-12-16

Category : Mathematics

ISBN : 1139495186

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Book Description

This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into finite-dimensional Euclidean spaces. The first part brings together a number of abstract embedding results, and provides a unified treatment of four definitions of dimension that arise in disparate fields: Lebesgue covering dimension (from classical 'dimension theory'), Hausdorff dimension (from geometric measure theory), upper box-counting dimension (from dynamical systems), and Assouad dimension (from the theory of metric spaces). These abstract embedding results are applied in the second part of the book to the finite-dimensional global attractors that arise in certain infinite-dimensional dynamical systems, deducing practical consequences from the existence of such attractors: a version of the Takens time-delay embedding theorem valid in spatially extended systems, and a result on parametrisation by point values. This book will appeal to all researchers with an interest in dimension theory, particularly those working in dynamical systems.



Dimensions, Embeddings, and Attractors

Author : James Cooper Robinson

Publisher :

Page : 219 pages

File Size : 34,93 MB

Release : 2014-05-14

Category : Attractors (Mathematics)

ISBN : 9780511933530

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Book Description

Accessible monograph exploring what it means for a set to be 'finite-dimensional' and applying the abstract theory to attractors.



Attractor Dimension Estimates for Dynamical Systems: Theory and Computation

Author : Nikolay Kuznetsov

Publisher : Springer Nature

Page : 555 pages

File Size : 11,32 MB

Release : 2020-07-02

Category : Computers

ISBN : 3030509877

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Book Description

This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.



Coherence in Three-Dimensional Category Theory

Author : Nick Gurski

Publisher : Cambridge University Press

Page : 287 pages

File Size : 37,16 MB

Release : 2013-03-21

Category : Mathematics

ISBN : 1107034892

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Book Description

Serves as an introduction to higher categories as well as a reference point for many key concepts in the field.



Malliavin Calculus for Lévy Processes and Infinite-Dimensional Brownian Motion

Author : Horst Osswald

Publisher : Cambridge University Press

Page : 429 pages

File Size : 13,42 MB

Release : 2012-03

Category : Mathematics

ISBN : 1107016142

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Book Description

After functional, measure and stochastic analysis prerequisites, the author covers chaos decomposition, Skorohod integral processes, Malliavin derivative and Girsanov transformations.



Topology and Dynamics of Chaos

Author : Christophe Letellier

Publisher : World Scientific

Page : 362 pages

File Size : 25,94 MB

Release : 2013

Category : Science

ISBN : 9814434868

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Book Description

The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included. The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto RAssler, Ren(r) Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively. Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical OCo not necessarily widely known OCo contributions (about the different types of chaos introduced by RAssler and not just the RAssler attractor; Gumowski and Mira's contributions in electronics; Poincar(r)'s heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology,



Fractal Geometry and Stochastics VI

Author : Uta Freiberg

Publisher : Springer Nature

Page : 307 pages

File Size : 10,98 MB

Release : 2021-03-23

Category : Mathematics

ISBN : 3030596494

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Book Description

This collection of contributions originates from the well-established conference series "Fractal Geometry and Stochastics" which brings together researchers from different fields using concepts and methods from fractal geometry. Carefully selected papers from keynote and invited speakers are included, both discussing exciting new trends and results and giving a gentle introduction to some recent developments. The topics covered include Assouad dimensions and their connection to analysis, multifractal properties of functions and measures, renewal theorems in dynamics, dimensions and topology of random discrete structures, self-similar trees, p-hyperbolicity, phase transitions from continuous to discrete scale invariance, scaling limits of stochastic processes, stemi-stable distributions and fractional differential equations, and diffusion limited aggregation. Representing a rich source of ideas and a good starting point for more advanced topics in fractal geometry, the volume will appeal to both established experts and newcomers.



Advances in Variational and Hemivariational Inequalities

Author : Weimin Han

Publisher : Springer

Page : 389 pages

File Size : 21,25 MB

Release : 2015-03-02

Category : Mathematics

ISBN : 3319144901

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Book Description

This volume is comprised of articles providing new results on variational and hemivariational inequalities with applications to Contact Mechanics unavailable from other sources. The book will be of particular interest to graduate students and young researchers in applied and pure mathematics, civil, aeronautical and mechanical engineering, and can be used as supplementary reading material for advanced specialized courses in mathematical modeling. New results on well posedness to stationary and evolutionary inequalities and their rigorous proofs are of particular interest to readers. In addition to results on modeling and abstract problems, the book contains new results on the numerical methods for variational and hemivariational inequalities.



Further Developments in Fractals and Related Fields

Author : Julien Barral

Publisher : Springer Science & Business Media

Page : 296 pages

File Size : 33,4 MB

Release : 2013-02-20

Category : Mathematics

ISBN : 081768400X

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Book Description

This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, “Fractals and Related Fields II,” held in June 2011. The book provides readers with an overview of developments in the mathematical fields related to fractals, including original research contributions as well as surveys from many of the leading experts on modern fractal theory and applications. The chapters cover fields related to fractals such as: *geometric measure theory *ergodic theory *dynamical systems *harmonic and functional analysis *number theory *probability theory Further Developments in Fractals and Related Fields is aimed at pure and applied mathematicians working in the above-mentioned areas as well as other researchers interested in discovering the fractal domain. Throughout the volume, readers will find interesting and motivating results as well as new avenues for further research.



Fractal Geometry and Stochastics V

Author : Christoph Bandt

Publisher : Birkhäuser

Page : 339 pages

File Size : 49,73 MB

Release : 2015-07-08

Category : Mathematics

ISBN : 3319186604

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Book Description

This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five topical sections: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. Each part starts with a state-of-the-art survey followed by papers covering a specific aspect of the topic. The authors are leading world experts and present their topics comprehensibly and attractively. Both newcomers and specialists in the field will benefit from this book.