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Exponentially Long Equilibrium Times in a One Dimensional Collisional Modelof Classical Gas
  • Language: en
  • Pages: 19
Hamiltonian Dynamics - Theory and Applications
  • Language: en
  • Pages: 187

Hamiltonian Dynamics - Theory and Applications

  • Type: Book
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  • Published: 2005-01-14
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  • Publisher: Springer

This volume compiles three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim is to describe the state of the art for some interesting problems, such as the Hamiltonian theory for infinite-dimensional Hamiltonian systems, including KAM theory, the recent extensions of the theory of adiabatic invariants, and the phenomena related to stability over exponentially long times of Nekhoroshev's theory. The books may serve as an excellent basis for young researchers, who will find here a complete and accurate exposition of recent original results and many hints for further investigation.

Molecular Networking
  • Language: en
  • Pages: 331

Molecular Networking

  • Type: Book
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  • Published: 2025-01-29
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  • Publisher: CRC Press

The book builds on the analogy between social groups and assemblies of molecules to introduce the concepts of statistical mechanics, machine learning and data science. Applying a data analytics approach to molecular systems, we show how individual (molecular) features and interactions between molecules, or "communication" processes, allow for the prediction of properties and collective behavior of molecular systems - just as polling and social networking shed light on the behavior of social groups. Applications to systems at the cutting-edge of research for biological, environmental, and energy applications are also presented. Key features: Draws on a data analytics approach of molecular systems. Covers hot topics such as artificial intelligence and machine learning of molecular trends. Contains applications to systems at the cutting-edge of research for biological, environmental and energy applications. Discusses molecular simulation and links with other important, emerging techniques and trends in computational sciences and society. Authors have a well-established track record and reputation in the field.

Impact of Modern Dynamics in Astronomy
  • Language: en
  • Pages: 468

Impact of Modern Dynamics in Astronomy

Modem dynamics is increasingly participating in the solution of problems raised by as tronomical observations. This new relationship is being fostered on one side by the im provements in the observations, which in recent years contributed several discoveries of new systems, such as the objects in the Kuiper belt, the pulsar and star companions, to speak only of the most striking ones, and, on the other hand, by the progresses in modem dynamics. The progresses in modem dynamics are due to two factors: the dissemination of fast computers, allowing the numerical studies of very complex systems by a large number of scientists, and the improvement in our understanding of the complex behaviour of Hamiltonian systems. KAM and Nekhorochev theories have shed a light on the subtle and surprizing interplays between regular and chaotic motions; numerical experiments and analytical approximations have shown how these peculiarities are indeed present in astronomically important systems and are instrumental in understanding their formation and evolution.

Notes on Hamiltonian Dynamical Systems
  • Language: en
  • Pages: 473

Notes on Hamiltonian Dynamical Systems

Introduces Hamiltonian dynamics from the very beginning, culminating in the most important recent results: Kolmogorov's and Nekhoroshev's.

Chaotic Oscillators
  • Language: en
  • Pages: 672

Chaotic Oscillators

This volume brings together a comprehensive selection of over fifty reprints on the theory and applications of chaotic oscillators. Included are fundamental mathematical papers describing methods for the investigation of chaotic behavior in oscillatory systems as well as the most important applications in physics and engineering. There is currently no book similar to this collection.

Simulation And Control Of Chaotic Nonequilibrium Systems: With A Foreword By Julien Clinton Sprott
  • Language: en
  • Pages: 325

Simulation And Control Of Chaotic Nonequilibrium Systems: With A Foreword By Julien Clinton Sprott

This book aims to provide a lively working knowledge of the thermodynamic control of microscopic simulations, while summarizing the historical development of the subject, along with some personal reminiscences. Many computational examples are described so that they are well-suited to learning by doing. The contents enhance the current understanding of the reversibility paradox and are accessible to advanced undergraduates and researchers in physics, computation, and irreversible thermodynamics.

Stability and Chaos in Celestial Mechanics
  • Language: en
  • Pages: 265

Stability and Chaos in Celestial Mechanics

This overview of classical celestial mechanics focuses the interplay with dynamical systems. Paradigmatic models introduce key concepts – order, chaos, invariant curves and cantori – followed by the investigation of dynamical systems with numerical methods.

Seminar on Dynamical Systems
  • Language: en
  • Pages: 297

Seminar on Dynamical Systems

  • Type: Book
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  • Published: 2013-06-29
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  • Publisher: Birkhäuser

The "Dynamical Systems Semester" took place at the Euler International Mathematical Institute in St. Petersburg, Russia, in the autumn of 1991. There were two workshops, October 14-25 and November 18-29, with more than 60 participants giving 70 talks. The titles of all talks are given at the end of this volume. Here we included 22 papers prepared by the authors especially for this volume, while the material of the other talks are published elsewhere. The semester was sponsored by the Soviet Academy of Sciences and UN ESCO. Since the new building of the Euler Institute was not ready at that moment, the sessions were held in the old building of the Steklov Mathemati cal Institute in the very center of St. Petersburg. Members of the staff of the Euler Institute were doing their best to organize properly the normal processing of the conference-not a simple task at that time because of the complications in the political and economical life in Russia just between the coup d'etat in August and the dismantling of the Soviet Union in December. We are thankful to all of them.