Download or read book Non integrable Dynamics written by József Beck and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Very little is known about non-integrable dynamical systems, a subject on the borderline of mathematics and physics. This is an attempt to give a first coherent description of a new and extremely exciting aspect of this subject This is a book on some flat dynamical systems which can be read without any background of ergodic theory The only technical requirement is a basic understanding of some basic linear algebra and elementary number theory The authors take great care in introducing the ideas at a leisurely pace, and often explain the main ideas by studying some examples The ideas are further illustrated by over 200 figures The book is accessible to a beginning graduate student as well as any interested experienced researcher"--
Download or read book Non integrable Dynamics Time quantitative Results written by Jozsef Beck and published by World Scientific. This book was released on 2023-08-24 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this monograph is to describe orbits of slowly chaotic motion. The study of geodesic flow on the unit torus is motivated by the irrational rotation sequence, where the most outstanding result is the Kronecker-Weyl equidistribution theorem and its time-quantitative enhancements, including superuniformity. Another important result is the Khinchin density theorem on superdensity, a best possible form of time-quantitative density. The purpose of this monograph is to extend these classical time-quantitative results to some non-integrable flat dynamical systems.The theory of dynamical systems is on the most part about the qualitative behavior of typical orbits and not about individual orbits. Thus, our study deviates from, and indeed is in complete contrast to, what is considered the mainstream research in dynamical systems. We establish non-trivial results concerning explicit individual orbits and describe their long-term behavior in a precise time-quantitative way. Our non-ergodic approach gives rise to a few new methods. These are based on a combination of ideas in combinatorics, number theory, geometry and linear algebra.Approximately half of this monograph is devoted to a time-quantitative study of two concrete simple non-integrable flat dynamical systems. The first concerns billiard in the L-shape region which is equivalent to geodesic flow on the L-surface. The second concerns geodesic flow on the surface of the unit cube. In each, we give a complete description of time-quantitative equidistribution for every geodesic with a quadratic irrational slope.
Download or read book Economic Dynamics written by Giancarlo Gandolfo and published by Springer Science & Business Media. This book was released on 1997 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treating the mathematical methods used in the economic dynamics, this book shows how they are utilised to build and analyse dynamical models. Accordingly, the focus is on the methods, and every new mathematical technique introduced is followed by its application to select economic models. The mathematical methods coveredc range from elementary linear difference and differential equations and simultaneous systems to the qualitative analysis of non-linear dynamical systems. Stability considerations are stressed throughout, including many advanced topics. Bifurcation and chaos theory are also dealt with. The reader is guided through a step-by-step analysis of each topic, be it a mathematical method or an economic model. The Study Edition also provides the reader with solutions to the numerous exercises.
Download or read book Qualitative and Quantitative Behaviour of Planetary Systems written by Rudolf Dvorak and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Third Alexander von Humboldt Colloquium on Celestial Mechanics
Download or read book IUTAM Symposium on Dynamics and Control of Nonlinear Systems with Uncertainty written by H.Y. Hu and published by Springer Science & Business Media. This book was released on 2007-07-26 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a state-of-the-art treatise on the problems of both nonlinearity and uncertainty in the dynamics and control of engineering systems. The concept of dynamics and control implies the combination of dynamic analysis and control synthesis. It is essential to gain insight into the dynamics of a nonlinear system with uncertainty if any new control strategy is designed to utilize nonlinearity.
Download or read book Computational Fluid Dynamics 2000 written by Nobuyuki Satofuka and published by Springer Science & Business Media. This book was released on 2001-08-29 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings contain a selection of refereed contributions as a source of reference for all those interested in the state of the art in computational fluid dynamics. The conference brings together physicists, mathematicians and engineers to review and share recent advances in the field.
Download or read book Chaotic Fractional and Complex Dynamics New Insights and Perspectives written by Mark Edelman and published by Springer. This book was released on 2017-11-17 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents nonlinear, chaotic and fractional dynamics, complex systems and networks, together with cutting-edge research on related topics. The fifteen chapters – written by leading scientists working in the areas of nonlinear, chaotic, and fractional dynamics, as well as complex systems and networks – offer an extensive overview of cutting-edge research on a range of topics, including fundamental and applied research. These include but are not limited to, aspects of synchronization in complex dynamical systems, universality features in systems with specific fractional dynamics, and chaotic scattering. As such, the book provides an excellent and timely snapshot of the current state of research, blending the insights and experiences of many prominent researchers.
Download or read book Dynamics and Evolution of Minor Bodies with Galactic and Geological Implications written by S.V.M. Clube and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Minor bodies in the Solar System, though representing only a small fraction of the mass in the Solar System, may well play a fundamental role in terrestrial evolution. This book contains investigations of the dynamics and physics of comets, asteroids and meteor streams, and the rather controversial topic of periodic phenomena in the Solar System as signified by geological records, together with several associated developments in celestial dynamics. All these problems are interwoven. This book makes a contribution towards unravelling the nature of the interactions between the Earth and its celestial environment.
Download or read book La Rivista del Nuovo cimento written by and published by . This book was released on 1999 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Annual Report written by Robert A. Welch Foundation and published by . This book was released on 1999 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Acta Physica Polonica written by and published by . This book was released on 1990-04 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Chinese Journal of Contemporary Mathematics written by and published by . This book was released on 2000 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Chaos Detection and Predictability written by Charalampos (Haris) Skokos and published by Springer. This book was released on 2016-03-04 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics. To address these issues there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, i.e. the computation of Lyapunov exponents, however, may suffer a number of problems and drawbacks, for example when applied to noisy experimental data. In the last two decades, several novel methods have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes and tutorial reviews serves as an introduction to and overview of modern chaos detection and predictability techniques for graduate students and non-specialists. The book covers theoretical and computational aspects of traditional methods to calculate Lyapunov exponents, as well as of modern techniques like the Fast (FLI), the Orthogonal (OFLI) and the Relative (RLI) Lyapunov Indicators, the Mean Exponential Growth factor of Nearby Orbits (MEGNO), the Smaller (SALI) and the Generalized (GALI) Alignment Index and the ‘0-1’ test for chaos.
Download or read book Local and Semi Local Bifurcations in Hamiltonian Dynamical Systems written by Heinz Hanßmann and published by Springer. This book was released on 2006-10-18 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.
Download or read book Wolf Prize in Mathematics written by Shiing-Shen Chern and published by World Scientific. This book was released on 2000 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Ecosystem Theories and Management written by Felix Muller and published by CRC Press. This book was released on 2000-02-10 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: As part of the Environmental and Ecological Modeling Handbooks series, the Handbook of Ecosystem Theories and Management provides a comprehensive overview of ecosystem theory and the tools - ecological engineering, ecological modeling, ecotoxicology and ecological economics -to manage these systems. The book is laid out to provide a summary or survey of each topic, using many tables and figures. Concepts, definitions, important findings, basic hypotheses, important correlations between theories and observation with illustrative graphs are included. The comprehensive treatment of ecosystem theory and application of theoretical tools, and the integration of classical theory and real world examples, sets this book apart. It covers newly emerging topical areas as well as nontraditional topical areas (i.e. chaos) that will interest professionals trained in previous decades and enlighten those now entering into formal training. The general approach taken by the authors makes this an essential reference and handbook for professionals and students.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt:
