New Trends in One-Dimensional Dynamics
New Trends in One-Dimensional Dynamics

Author: Maria José Pacifico

Publisher: Springer Nature

Published: 2019-12-14

Total Pages: 333

ISBN-13: 3030168336

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This volume presents the proceedings of the meeting New Trends in One-Dimensional Dynamics, which celebrated the 70th birthday of Welington de Melo and was held at the IMPA, Rio de Janeiro, in November 2016. Highlighting the latest results in one-dimensional dynamics and its applications, the contributions gathered here also celebrate the highly successful meeting, which brought together experts in the field, including many of Welington de Melo’s co-authors and former doctoral students. Sadly, Welington de Melo passed away shortly after the conference, so that the present volume became more a tribute to him. His role in the development of mathematics was undoubtedly an important one, especially in the area of low-level dynamics, and his legacy includes, in addition to many articles with fundamental contributions, books that are required reading for all newcomers to the field.

Mathematical Tools for One-Dimensional Dynamics
Mathematical Tools for One-Dimensional Dynamics

Author: Edson de Faria

Publisher: Cambridge University Press

Published: 2008-10-02

Total Pages: 192

ISBN-13: 1139474847

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Originating with the pioneering works of P. Fatou and G. Julia, the subject of complex dynamics has seen great advances in recent years. Complex dynamical systems often exhibit rich, chaotic behavior, which yields attractive computer generated pictures, for example the Mandelbrot and Julia sets, which have done much to renew interest in the subject. This self-contained book discusses the major mathematical tools necessary for the study of complex dynamics at an advanced level. Complete proofs of some of the major tools are presented; some, such as the Bers-Royden theorem on holomorphic motions, appear for the very first time in book format. An appendix considers Riemann surfaces and Teichmüller theory. Detailing the very latest research, the book will appeal to graduate students and researchers working in dynamical systems and related fields. Carefully chosen exercises aid understanding and provide a glimpse of further developments in real and complex one-dimensional dynamics.

One-Dimensional Dynamics
One-Dimensional Dynamics

Author: Welington de Melo

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 616

ISBN-13: 3642780431

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One-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and complete proofs of many results. To show what results one might expect, the first chapter deals with the theory of circle diffeomorphisms. The remainder of the book is an attempt to develop the analogous theory in the non-invertible case, despite the intrinsic additional difficulties. In this way, we have tried to show that there is a unified theory in one-dimensional dynamics. By reading one or more of the chapters, the reader can quickly reach the frontier of research. Let us quickly summarize the book. The first chapter deals with circle diffeomorphisms and contains a complete proof of the theorem on the smooth linearizability of circle diffeomorphisms due to M. Herman, J.-C. Yoccoz and others. Chapter II treats the kneading theory of Milnor and Thurstonj also included are an exposition on Hofbauer's tower construction and a result on fuB multimodal families (this last result solves a question posed by J. Milnor).

Recent Trends In Chaotic, Nonlinear And Complex Dynamics
Recent Trends In Chaotic, Nonlinear And Complex Dynamics

Author: Jan Awrejcewicz

Publisher: World Scientific

Published: 2021-07-26

Total Pages: 561

ISBN-13: 981122191X

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In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.

Hyperbolic Dynamics, Fluctuations and Large Deviations
Hyperbolic Dynamics, Fluctuations and Large Deviations

Author: D. Dolgopyat

Publisher: American Mathematical Soc.

Published: 2015-04-01

Total Pages: 354

ISBN-13: 1470411121

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This volume contains the proceedings of the semester-long special program on Hyperbolic Dynamics, Large Deviations and Fluctuations, which was held from January-June 2013, at the Centre Interfacultaire Bernoulli, École Polytechnique Fédérale de Lausanne, Switzerland. The broad theme of the program was the long-term behavior of dynamical systems and their statistical behavior. During the last 50 years, the statistical properties of dynamical systems of many different types have been the subject of extensive study in statistical mechanics and thermodynamics, ergodic and probability theories, and some areas of mathematical physics. The results of this study have had a profound effect on many different areas in mathematics, physics, engineering and biology. The papers in this volume cover topics in large deviations and thermodynamics formalism and limit theorems for dynamic systems. The material presented is primarily directed at researchers and graduate students in the very broad area of dynamical systems and ergodic theory, but will also be of interest to researchers in related areas such as statistical physics, spectral theory and some aspects of number theory and geometry.

Deterministic Chaos In One Dimensional Continuous Systems
Deterministic Chaos In One Dimensional Continuous Systems

Author: Jan Awrejcewicz

Publisher: World Scientific

Published: 2016-03-14

Total Pages: 577

ISBN-13: 9814719714

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This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations.Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler-Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic-plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels.The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering.

Advances and New Trends in Environmental Informatics
Advances and New Trends in Environmental Informatics

Author: Andreas Kamilaris

Publisher: Springer Nature

Published: 2020-12-16

Total Pages: 269

ISBN-13: 3030619699

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This book is an outcome of the 34th International Conference EnviroInfo 2020, hosted virtually in Nicosia, Cyprus by the Research Centre on Interactive Media, Smart Systems and Emerging Technologies (RISE). It presents a selection of papers that describe innovative scientific approaches and ongoing research in environmental informatics and the emerging field of environmental sustainability, promoted and facilitated by the use of information and communication technologies (ICT). The respective articles cover a broad range of scientific aspects including advances in core environmental informatics-related technologies such as earth observation, environmental modelling, big data and machine learning, robotics, smart agriculture and food solutions, renewable energy-based solutions, optimization of infrastructures, sustainable industrial processes, and citizen science, as well as applications of ICT solutions intended to support societal transformation processes toward the more sustainable management of resource use, transportation and energy supplies. Given its scope, the book is essential reading for scientists, experts and students in these fields of research. Chapter “Developing a Configuration System for a Simulation Game in the Domain of Urban CO2 Emissions Reduction” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

New Trends in Kramers’ Reaction Rate Theory
New Trends in Kramers’ Reaction Rate Theory

Author: P. Talkner

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 258

ISBN-13: 9401104654

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The escape from metastable states via noise-assisted hopping and/or tunneling is pivotal to many scientific disciplines. It impacts on such diverse physical, chemical and biological processes as diffusion in solids, chemical reactions, nucleation phenomena and transfer of matter and information in biological systems. This volume surveys recent developments in the rate theory of both equilibrium and nonequilibrium processes. The understanding of the classical and quantum-mechanical concepts of this theory is deepened and extended in order to cope with various problems which, in particular, arise in complex systems. A wide range of applications are discussed such as correlated hops in periodic potentials, fluctuating barriers, transitions to limit cycles, discrete time dynamics, random walks on selfsimilar structures, and nonexponential decay in disordered systems is covered and profoundly discussed. For research workers and graduate students in chemistry, physics and biology with an interest in reaction rate theory.

Dynamics, Bifurcation and Symmetry
Dynamics, Bifurcation and Symmetry

Author: Pascal Chossat

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 355

ISBN-13: 9401109567

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This book collects contributions to the conference" Dynamics, Bifurcation and Symmetry, new trends and new tools", which was held at the Institut d'Etudes Sci entifiques de Cargese (France), September 3-9, 1993. The first aim of this conference was to gather and summarize the work of the European Bifurcation Theory Group after two years of existence (the EBTG links european laboratories in five countries via an EC grant). Thanks to a NATO ARW grant, the conference developed into an international meeting on bifurcation theory and dynamical systems, with the partic ipation of leading specialists not only from Europe but also from overseas countries (Canada, USA, South America). It was a great satisfaction to notice the active, and quite enthusiastic participation of many young scientists. This is reflected in the present book for which many contributors are PhD students or post-doc researchers. Although several "big" themes (bifurcation with symmetry, low dimensional dynam ics, dynamics in EDP's, applications, . . . ) are present in these proceedings, we have divided the book into corresponding parts. In fact these themes overlap in most contributions, which seems to reflect a general tendancy in nonlinear science. I am very pleased to thank for their support the NATO International Exchange Scientific Program as well as the EEC Science Program, which made possible the suc cess of this conference.

Perspectives in Fluid Dynamics
Perspectives in Fluid Dynamics

Author: G. K. Batchelor

Publisher: Cambridge University Press

Published: 2003

Total Pages: 650

ISBN-13: 9780521531696

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Paperback edition of text on fluid dynamics for graduate students and specialists alike.