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An Introduction to Dynamical Systems and Chaos, Second Edition

Posted By: AvaxGenius
Date: 24 Feb 2024 04:47:46
An Introduction to Dynamical Systems and Chaos, Second Edition

An Introduction to Dynamical Systems and Chaos, Second Edition by G. C. Layek
English | PDF EPUB (True) | 2024 | 701 Pages | ISBN : 9819976944 | 102.1 MB

This book discusses continuous and discrete nonlinear systems in systematic and sequential approaches. The unique feature of the book is its mathematical theories on flow bifurcations, nonlinear oscillations, Lie symmetry analysis of nonlinear systems, chaos theory, routes to chaos and multistable coexisting attractors. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, featuring a multitude of detailed worked-out examples alongside comprehensive exercises. The book is useful for courses in dynamical systems and chaos and nonlinear dynamics for advanced undergraduate, graduate and research students in mathematics, physics and engineering.
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Order and Chaos in Dynamical Astronomy

Posted By: AvaxGenius
Date: 28 Jan 2024 15:18:34
Order and Chaos in Dynamical Astronomy

Order and Chaos in Dynamical Astronomy by George Contopoulos
English | PDF | 2002 | 633 Pages | ISBN : 3540433600 | 57.8 MB

There have been many books on Dynamical Astronomy up to now. Many are devoted to Celestial Mechanics, but there are also several books on Stellar and Galactic Dynamics. The first books on stellar dynamics dealt mainly with the statistics of stellar motions (e. g. Smart's "Stellar Dynamics" (1938), or Trumpler and Weaver's "Statistical Astronomy" (1953)). A classical book in this field is Chandrasekhar's "Principles of Stellar Dynamics" (1942) that dealt mainly with the time of relaxation, the solutions of Liouville's equation, and the dynamics of clusters. In the Dover edition of this book (1960) an extended Appendix was added, containing the statistical mechanics of stellar systems, a quite "modern" subject at that time. The need for a classroom book was covered for several years by the book of Mihalas and Routly "Galactic Astronomy" (1969).
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Bifurcation, Symmetry and Patterns

Posted By: AvaxGenius
Date: 28 Jan 2024 05:07:07
Bifurcation, Symmetry and Patterns

Bifurcation, Symmetry and Patterns by Jorge Buescu, Sofia B. S. D. Castro, Ana Paula Silva Dias, Isabel Salgado Labouriau
English | PDF | 2003 | 215 Pages | ISBN : 3764370203 | 20 MB

This book represents the latest developments on both the theory and applications of bifurcations with symmetry. It includes recent experimental work as well as new approaches to and applications of the theory to other sciences. It shows the range of dissemination of the work of Martin Golubitsky and Ian Stewart and its influence in modern mathematics at the same time as it contains work of young mathematicians in new directions. The range of topics includes mathematical biology, pattern formation, ergodic theory, normal forms, one-dimensional dynamics and symmetric dynamics.
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Handbook of Dynamic Data Driven Applications Systems: Volume 2 (Repost)

Posted By: AvaxGenius
Date: 3 Jan 2024 05:46:34
Handbook of Dynamic Data Driven Applications Systems: Volume 2 (Repost)

Handbook of Dynamic Data Driven Applications Systems: Volume 2 by Frederica Darema, Erik P. Blasch, Sai Ravela, Alex J. Aved
English | EPUB (True) | 2023 | 937 Pages | ISBN : 3031279859 | 138.1 MB

This Second Volume in the series Handbook of Dynamic Data Driven Applications Systems (DDDAS) expands the scope of the methods and the application areas presented in the first Volume and aims to provide additional and extended content of the increasing set of science and engineering advances for new capabilities enabled through DDDAS. The methods and examples of breakthroughs presented in the book series capture the DDDAS paradigm and its scientific and technological impact and benefits. The DDDAS paradigm and the ensuing DDDAS-based frameworks for systems’ analysis and design have been shown to engender new and advanced capabilities for understanding, analysis, and management of engineered, natural, and societal systems (“applications systems”), and for the commensurate wide set of scientific and engineering fields and applications, as well as foundational areas.
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Chaotic Dynamics in Planetary Systems

Posted By: AvaxGenius
Date: 1 Jan 2024 14:37:29
Chaotic Dynamics in Planetary Systems

Chaotic Dynamics in Planetary Systems by Sylvio Ferraz-Mello
English | PDF EPUB (True) | 2024 | 175 Pages | ISBN : 303145815X | 32.2 MB

The main theme of the book is the presentation of techniques used to identify chaotic behavior in the evolution of conservative mechanical systems and their application to astronomical systems. It results from graduate courses given by the author over the years both at university and at several international summer schools.
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Handbook of Dynamic Data Driven Applications Systems: Volume 2

Posted By: AvaxGenius
Date: 16 Sep 2023 03:45:09
Handbook of Dynamic Data Driven Applications Systems: Volume 2

Handbook of Dynamic Data Driven Applications Systems: Volume 2 by Frederica Darema, Erik P. Blasch, Sai Ravela, Alex J. Aved
English | PDF EPUB (True) | 2023 | 937 Pages | ISBN : 3031279859 | 169.6 MB

This Second Volume in the series Handbook of Dynamic Data Driven Applications Systems (DDDAS) expands the scope of the methods and the application areas presented in the first Volume and aims to provide additional and extended content of the increasing set of science and engineering advances for new capabilities enabled through DDDAS. The methods and examples of breakthroughs presented in the book series capture the DDDAS paradigm and its scientific and technological impact and benefits. The DDDAS paradigm and the ensuing DDDAS-based frameworks for systems’ analysis and design have been shown to engender new and advanced capabilities for understanding, analysis, and management of engineered, natural, and societal systems (“applications systems”), and for the commensurate wide set of scientific and engineering fields and applications, as well as foundational areas.
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Geometric Mechanics

Posted By: AvaxGenius
Date: 26 Aug 2023 15:43:31
Geometric Mechanics

Geometric Mechanics by Waldyr Muniz Oliva
English | PDF | 2002 | 273 Pages | ISBN : 3540442421 | 3.2 MB

Geometric Mechanics here means mechanics on a pseudo-riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems. The first seven chapters are written in the spirit of Newtonian Mechanics while the last two ones as well as two of the four appendices describe the foundations and some aspects of Special and General Relativity. All the material has a coordinate free presentation but, for the sake of motivation, many examples and exercises are included in order to exhibit the desirable flavor of physical applications.
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Classical Mechanics: Systems of Particles and Hamiltonian Dynamics

Posted By: AvaxGenius
Date: 26 Aug 2023 14:17:17
Classical Mechanics: Systems of Particles and Hamiltonian Dynamics

Classical Mechanics: Systems of Particles and Hamiltonian Dynamics by Walter Greiner
English | PDF (True) | 2010 | 574 Pages | ISBN : 3642034330 | 7.5 MB

This textbook Classical Mechanics provides a complete survey on all aspects of classical mechanics in theoretical physics. An enormous number of worked examples and problems show students how to apply the abstract principles to realistic problems.
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Local Limit Theorems for Inhomogeneous Markov Chains

Posted By: AvaxGenius
Date: 2 Aug 2023 00:26:34
Local Limit Theorems for Inhomogeneous Markov Chains

Local Limit Theorems for Inhomogeneous Markov Chains by Dmitry Dolgopyat , Omri M. Sarig
English | PDF | 2023 | 348 Pages | ISBN : 3031326008 | 10 MB

This book extends the local central limit theorem to Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. The book develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains.
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Flows on Compact Surfaces: The Weil–Hedlund–Anosov Program

Posted By: AvaxGenius
Date: 20 Jul 2023 01:44:57
Flows on Compact Surfaces: The Weil–Hedlund–Anosov Program

Flows on Compact Surfaces: The Weil–Hedlund–Anosov Program by Nelson G. Markley , Mary Vanderschoot
English | PDF EPUB (True) | 2023 | 368 Pages | ISBN : 3031329546 | 49.5 MB

This textbook offers a uniquely accessible introduction to flows on compact surfaces, filling a gap in the existing literature. The book can be used for a single semester course and/or for independent study. It demonstrates that covering spaces provide a suitable and modern setting for studying the structure of flows on compact surfaces. The thoughtful treatment of flows on surfaces uses topology (especially covering spaces), the classification of compact surfaces, and Euclidean and hyperbolic rigid motions to establish structural theorems that describe flows on surfaces generally. Several of the topics from dynamical systems that appear in this book (e.g., fixed points, invariant sets, orbits, almost periodic points) also appear in the many subareas of dynamical systems. The book successfully presents the reader with a self-contained introduction to dynamical systems or an expansion of one's existing knowledge of the field. Prerequisites include completion of a graduate-level topology course; a background in dynamical systems is not assumed.
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Geometric and Ergodic Aspects of Group Actions (Repost)

Posted By: AvaxGenius
Date: 9 Jun 2022 11:25:45
Geometric and Ergodic Aspects of Group Actions (Repost)

Geometric and Ergodic Aspects of Group Actions by S. G. Dani
English | PDF | 2019 | 176 Pages | ISBN : 9811506825 | 5.3 MB

This book gathers papers on recent advances in the ergodic theory of group actions on homogeneous spaces and on geometrically finite hyperbolic manifolds presented at the workshop “Geometric and Ergodic Aspects of Group Actions,” organized by the Tata Institute of Fundamental Research, Mumbai, India, in 2018. Written by eminent scientists, and providing clear, detailed accounts of various topics at the interface of ergodic theory, the theory of homogeneous dynamics, and the geometry of hyperbolic surfaces, the book is a valuable resource for researchers and advanced graduate students in mathematics.
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Linearization Models for Complex Dynamical Systems (Repost)

Posted By: AvaxGenius
Date: 16 Apr 2022 15:16:43
Linearization Models for Complex Dynamical Systems (Repost)

Linearization Models for Complex Dynamical Systems: Topics in Univalent Functions, Functional Equations and Semigroup Theory Mark Elin by David Shoikhet
English | PDF | 2010 | 271 Pages | ISBN : 3034605080 | 2 MB

This book provides valuable insights into complex analysis, dynamical systems, geometric function theory and operator theory. Intended for a broad spectrum of readers, ranging from undergraduate and graduate mathematics students to active researchers, it offers extensive coverage of recent advances in geometric function theory, including the theory of starlike and spirallike functions with respect to a boundary point. Of particular interest is its treatment of continuous time semigroups, about which little has been previously known, emphasizing the use of generation theory for continuous dynamical systems.
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Dynamically Coupled Rigid Body-Fluid Flow Systems

Posted By: AvaxGenius
Date: 28 Oct 2021 23:37:13
Dynamically Coupled Rigid Body-Fluid Flow Systems

Dynamically Coupled Rigid Body-Fluid Flow Systems by Banavara N. Shashikanth
English | PDF,EPUB | 2021 | 192 Pages | ISBN : 3030826457 | 17.8 MB

This book presents a unified study of dynamically coupled systems involving a rigid body and an ideal fluid flow from the perspective of Lagrangian and Hamiltonian mechanics. It compiles theoretical investigations on the topic of dynamically coupled systems using a framework grounded in Kirchhoff’s equations.
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Geometric Integrators for Differential Equations with Highly Oscillatory Solutions

Posted By: AvaxGenius
Date: 29 Sep 2021 02:40:54
Geometric Integrators for Differential Equations with Highly Oscillatory Solutions

Geometric Integrators for Differential Equations with Highly Oscillatory Solutions by Xinyuan Wu
English | PDF,EPUB | 2021 | 507 Pages | ISBN : 9811601461 | 90.7 MB

The idea of structure-preserving algorithms appeared in the 1980's. The new paradigm brought many innovative changes. The new paradigm wanted to identify the long-time behaviour of the solutions or the existence of conservation laws or some other qualitative feature of the dynamics. Another area that has kept growing in importance within Geometric Numerical Integration is the study of highly-oscillatory problems:
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Discontinuous Dynamical Systems on Time-varying Domains

Posted By: AvaxGenius
Date: 23 May 2021 20:44:15
Discontinuous Dynamical Systems on Time-varying Domains

Discontinuous Dynamical Systems on Time-varying Domains by Albert C. J. Luo
English | PDF | 2009 | 234 Pages | ISBN : 3642002528 | 28 MB

"Discontinuous Dynamical Systems on Time-varying Domains" is the first monograph focusing on this topic. While in the classic theory of dynamical systems the focus is on dynamical systems on time-invariant domains, this book presents discontinuous dynamical systems on time-varying domains where the corresponding switchability of a flow to the time-varying boundary in discontinuous dynamical systems is discussed.
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