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Author: József Beck
Publisher:
ISBN: 9789811273865
Category : Chaotic behavior in systems
Languages : en
Pages : 0
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Book Description
"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"--
Author: József Beck
Publisher:
ISBN: 9789811273865
Category : Chaotic behavior in systems
Languages : en
Pages : 0
Get Book Here
Book Description
"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"--
Author: Jozsef Beck
Publisher: World Scientific
ISBN: 9811273871
Category : Mathematics
Languages : en
Pages : 401
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Book Description
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.
Author: Victory Szebehely
Publisher: Elsevier
ISBN: 0323143466
Category : Science
Languages : en
Pages : 685
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Book Description
Theory of Orbits: The Restricted Problem of Three Bodies is a 10-chapter text that covers the significance of the restricted problem of three bodies in analytical dynamics, celestial mechanics, and space dynamics. The introductory part looks into the use of three essentially different approaches to dynamics, namely, the qualitative, the quantitative, and the formalistic. The opening chapters consider the formulation of equations of motion in inertial and in rotating coordinate systems, as well as the reductions of the problem of three bodies and the corresponding streamline analogies. These topics are followed by discussions on the regularization and writing of equations of motion in a singularity-free systems; the principal qualitative aspect of the restricted problem of the curves of zero velocity; and the motion and nonlinear stability in the neighborhood of libration points. This text further explores the principles of Hamiltonian dynamics and its application to the restricted problem in the extended phase space. A chapter treats the problem of two bodies in a rotating coordinate system and treats periodic orbits in the restricted problem. Another chapter focuses on the comparison of the lunar and interplanetary orbits in the Soviet and American literature. The concluding chapter is devoted to modifications of the restricted problem, such as the elliptic, three-dimensional, and Hill's problem. This book is an invaluable source for astronomers, engineers, and mathematicians.
Author: Alain Goriely
Publisher: World Scientific
ISBN: 981023533X
Category : Mathematics
Languages : en
Pages : 435
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Book Description
This invaluable book examines qualitative and quantitative methods for nonlinear differential equations, as well as integrability and nonintegrability theory. Starting from the idea of a constant of motion for simple systems of differential equations, it investigates the essence of integrability, its geometrical relevance and dynamical consequences. Integrability theory is approached from different perspectives, first in terms of differential algebra, then in terms of complex time singularities and finally from the viewpoint of phase geometry (for both Hamiltonian and non-Hamiltonian systems). As generic systems of differential equations cannot be exactly solved, the book reviews the different notions of nonintegrability and shows how to prove the nonexistence of exact solutions and/or a constant of motion. Finally, nonintegrability theory is linked to dynamical systems theory by showing how the property of complete integrability, partial integrability or nonintegrability can be related to regular and irregular dynamics in phase space.
Author: V.G. Szebehely
Publisher: Springer Science & Business Media
ISBN: 9401014930
Category : Science
Languages : en
Pages : 363
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Book Description
Proceedings of the NATO Advanced Study Institute, Cortina D'Ampezzo, Italy, August 3-16, 1975
Author: Rudolf Dvorak
Publisher: Springer Science & Business Media
ISBN: 9401120307
Category : Science
Languages : en
Pages : 394
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Book Description
Proceedings of the Third Alexander von Humboldt Colloquium on Celestial Mechanics
Author: Murray Muraskin
Publisher: World Scientific
ISBN: 9814500690
Category : Science
Languages : en
Pages : 232
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Book Description
Mathematical aesthetics is not discussed as a separate discipline in other books than this, even though it is reasonable to suppose that the foundations of physics lie in mathematical aesthetics. This book presents a list of mathematical principles that can be classified as “aesthetic” and shows that these principles can be cast into a nonlinear set of equations. Then, with this minimal input, the book shows that one can obtain lattice solutions, soliton systems, closed strings, instantons and chaotic-looking systems as well as multi-wave-packet solutions as output. These solutions have the common feature of being nonintegrable, i.e. the results of integration depend on the integration path. The topic of nonintegrable systems has not been given much attention in other books. Hence we discuss techniques for dealing with such systems.
Author: Rudolf Dvorak
Publisher: Springer Science & Business Media
ISBN: 9401155100
Category : Science
Languages : en
Pages : 424
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Book Description
It is now a well established tradition that every four years, at the end of winter, a group of "celestial mechanicians" from all over the world gather at the "Alpen gasthof Peter Rosegger" in the Styrian Alps (Ramsau, Austria). This time the colloquium was held from March 17 to March 23, 1996 and was devoted to the Dynamical Behaviour of our Planetary System. The papers covered a large range of questions of current interest: theoretical questions (re- nances, universal properties, non integrability, transport, ... ) and questions about numerical tools ( symplectic maps, indicators of chaos, ... ) were particularly well represented; the never ending problem of the sculpting of the asteroid belt was also qui te popular. You will find in the following pages a pot-pourri of what we listen to; you will miss of course the diversity of accents with which the tunes were delivered: from China, from Japan, from Brazil, from the United-States of America and from all over Europe, East and West. Let us not forget that the comet 199682 (Hyakutake) came to visit us; many an evening was spent on the deck of the Alpengasthof contemplating this celestial visitor who liked to play hide-and-seek behind the spruce trees.
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 568
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Book Description
Author: P. Kenneth Seidelmann
Publisher: Springer Science & Business Media
ISBN: 9400909853
Category : Science
Languages : en
Pages : 339
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Book Description
Proceedings of the 109th Colloquium of the International Astronomical Union, held in Gaithersburg, Maryland, 27-29 July, 1988
