Order and Chaos in Dynamical Astronomy

This book is one of the first to provide a general overview of order and chaos in dynamical astronomy.

Order and Chaos in Dynamical Astronomy

Author: George Contopoulos

Publisher: Springer Science & Business Media

ISBN: 3662049171

Page: 624

View: 220

This book is one of the first to provide a general overview of order and chaos in dynamical astronomy. The progress of the theory of chaos has a profound impact on galactic dynamics. It has even invaded celestial mechanics, since chaos was found in the solar system which in the past was considered as a prototype of order. The book provides a unifying approach to these topics from an author who has spent more than 50 years of research in the field. The first part treats order and chaos in general. The other two parts deal with order and chaos in galaxies and with other applications in dynamical astronomy, ranging from celestial mechanics to general relativity and cosmology.

Chaos in Astronomy

2.2 The Problem of Chaotic Orbits in Schwarzschild's Method Schwarzschild [3]
found it necessary to include chaotic orbits in his models but, then, these were
not fully stable. He built several models using orbits computed over a Hubble
time ...

Chaos in Astronomy

Author: G. Contopoulos

Publisher: Springer Science & Business Media

ISBN: 3540758267

Page: 497

View: 832

The conference 'Chaos in Astronomy' was held in Athens on 17-20 Sept. 2007. This book contains edited refereed contributions. It offers an overview to students and newcomers entering various fields of dynamical astronomy.

Adventures in Order and Chaos

In order to observe variable stars I spent one month at the astronomical station of
Penteli, on a hill outside Athens. There was no road (only a narrow path up the
hill), no electricity, no telephone, no running water (we brought water with a ...

Adventures in Order and Chaos

Author: George Contopoulos

Publisher: Springer Science & Business Media

ISBN: 1402030401

Page: 200

View: 99

For many years I was organizing a weekly seminar on dynamical astronomy, and I used to make some historical remarks on every subject, including some anecdotes from my contacts with many leading scientists over the years. I described also the development of various subjects and the emergence of new ideasindynamicalastronomy. Thenseveralpeoplepromptedmetowritedown these remarks, which cannot be found in papers, or books. Thus, I decided to write this book, which contains my experiences over the years. I hope that this book may be helpful to astronomy students all over the world. During my many years of teaching, as a visiting professor, in American Universities (1962-1994, Yale, Harvard, MIT, Cornell, Chicago, Maryland and Florida) I was impressed by the quality of my graduate students. Most of them were very bright, asking penetrating questions, and preparing their homework in a perfect way. In a few cases, instead of a ?nal examination, I assigned to them some small research projects and they presented their results at the end of the course. They were excellent in preparing the appropriate slides and in presenting their results in a concise and clear way.

Observational Manifestation of Chaos in Astrophysical Objects

This book addresses a broad range of problems related to observed manifestations of chaotic motions in galactic and stellar objects, by invoking basic theory, numerical modeling, and observational evidence.

Observational Manifestation of Chaos in Astrophysical Objects

Author: Alexei Fridman

Publisher: Springer Science & Business Media

ISBN: 9781402009358

Page: 138

View: 369

This book addresses a broad range of problems related to observed manifestations of chaotic motions in galactic and stellar objects, by invoking basic theory, numerical modeling, and observational evidence. For the first time, methods of stochastic dynamics are applied to actually observed astronomical objects, e.g. the gaseous disc of the spiral galaxy NGC 3631. In the latter case, the existence of chaotic trajectories in the boundary of giant vortices was recently found by the calculation of the Lyapunov characteristic number of these trajectories. The reader will find research results on the peculiarities of chaotic system behaviour; a study of the integrals of motion in self-consistent systems; numerical modeling results of the evolution process of disk systems involving resonance excitation of the density waves in spiral galaxies; a review of specific formations in stars and high-energy sources demonstrating their stochastic nature; a discussion of the peculiarities of the precessional motion of the accretion disk and relativistic jets in the double system SS 433; etc.

Chaos and Stability in Planetary Systems

As such, this volume is particularly suitable for those who need to understand the substantial connections between these different topics. This book is intended as an introduction to the field of planetary systems at the postgraduate level.

Chaos and Stability in Planetary Systems

Author: Rudolf Dvorak

Publisher: Springer Science & Business Media

ISBN: 9783540282082

Page: 281

View: 461

This book is intended as an introduction to the field of planetary systems at the postgraduate level. It consists of four extensive lectures on Hamiltonian dynamics, celestial mechanics, the structure of extrasolar planetary systems and the formation of planets. As such, this volume is particularly suitable for those who need to understand the substantial connections between these different topics.

Chaotic Modelling and Simulation

Analysis of Chaotic Models, Attractors and Forms Christos H. Skiadas, Charilaos
Skiadas ... astronomy and astrophysics from recent developments (the
Conference on Chaos in Astronomy organized by George Contopoulos in 2002
was very ...

Chaotic Modelling and Simulation

Author: Christos H. Skiadas

Publisher: CRC Press

ISBN: 9781420079012

Page: 364

View: 701

Offers Both Standard and Novel Approaches for the Modeling of Systems Examines the Interesting Behavior of Particular Classes of Models Chaotic Modelling and Simulation: Analysis of Chaotic Models, Attractors and Forms presents the main models developed by pioneers of chaos theory, along with new extensions and variations of these models. Using more than 500 graphs and illustrations, the authors show how to design, estimate, and test an array of models. Requiring little prior knowledge of mathematics, the book focuses on classical forms and attractors as well as new simulation methods and techniques. Ideas clearly progress from the most elementary to the most advanced. The authors cover deterministic, stochastic, logistic, Gaussian, delay, Hénon, Holmes, Lorenz, Rössler, and rotation models. They also look at chaotic analysis as a tool to design forms that appear in physical systems; simulate complicated and chaotic orbits and paths in the solar system; explore the Hénon–Heiles, Contopoulos, and Hamiltonian systems; and provide a compilation of interesting systems and variations of systems, including the very intriguing Lotka–Volterra system. Making a complex topic accessible through a visual and geometric style, this book should inspire new developments in the field of chaotic models and encourage more readers to become involved in this rapidly advancing area.

From Cosmos to Chaos

Looks at the role of probability in modern science. Using the developments in fundamental physics as examples, this book shows how central is the need to deal with uncertainty and incomplete knowledge.

From Cosmos to Chaos

Author: Peter Coles

Publisher: Oxford University Press on Demand

ISBN: 0198567626

Page: 216

View: 793

Looks at the role of probability in modern science. Using the developments in fundamental physics as examples, this book shows how central is the need to deal with uncertainty and incomplete knowledge. It also covers developments in physics, such as superstrings and dark energy, and draws lessons for everyday life.

Complex Systems Chaos and Beyond

While maintaining a high level of rigour, an overly complicated mathematical apparatus is avoided in order to make this book accessible, beyond the specialist level, to a wider interdisciplinary readership.

Complex Systems  Chaos and Beyond

Author: Kunihiko Kaneko

Publisher: Springer Science & Business Media

ISBN: 9783540672029

Page: 273

View: 438

Chaos in science has always been a fascinating realm since it challenges the usual scientific approach of reductionism. While carefully distinguishing between complexity, holism, randomness, incompleteness, nondeterminism and stochastic behaviour the authors show that, although many aspects of chaos have been phenomenologically understood, most of its defining principles are still difficult to grasp and formulate. Demonstrating that chaos escapes all traditional methods of description, the authors set out to find new methods to deal with this phenomenon and illustrate their constructive approach with many examples from physics, biology and information technology. While maintaining a high level of rigour, an overly complicated mathematical apparatus is avoided in order to make this book accessible, beyond the specialist level, to a wider interdisciplinary readership.

Quantum Signatures of Chaos

Now well established as a textbook in this rapidly developing field of research, the new edition is much enlarged and covers a host of new results.

Quantum Signatures of Chaos

Author: Fritz Haake

Publisher: Springer Science & Business Media

ISBN: 9783540677239

Page: 479

View: 399

This textbook provides an excellent introduction to a new and rapidly developing field of research. Now well established as a textbook in this rapidly developing field of research, the new edition is much enlarged and covers a host of new results.

Impact of Modern Dynamics in Astronomy

G.CONTOPOULOS1'2, N. VOGLIS2 and C. EFTHYMIOPOULOS1'2 1 Research
Center for Astronomy, Academy of Athens 2 Department of Astronomy, University
of Athens Abstract. Chaos appears in various problems of Relativity and ...

Impact of Modern Dynamics in Astronomy

Author: J. Henrard

Publisher: Springer Science & Business Media

ISBN: 9780792358428

Page: 466

View: 763

This volume of proceedings contains review and research papers concerning the impact of modern dynamics in astronomy. Modern dynamics is playing an increasing role in the solution of problems raised by astronomical observations. This new relationship is being fostered by discoveries of new systems, such as the Kuiper belt, pulsar and star companions; by progress in theoretical dynamics, like KAM and Nekhorochev theories and adiabatic invariants; and by the dissemination of fast computers. The two main areas of applications which are discussed are stellar systems, including dynamics of galaxies, and small bodies in the solar system. In both cases the concepts and tools of chaotic motion are considered and fully discussed.

The Oxford Guide to the History of Physics and Astronomy

54 CHAOS AND COMPLEXITY sity of California at Berkeley were developing
ways to model dynamical systems through topology, folding and stretching plots
in phase space to reproduce the unpredictable histories of nonlinear systems;
two ...

The Oxford Guide to the History of Physics and Astronomy

Author: J. L. Heilbron

Publisher: Oxford University Press on Demand

ISBN: 0195171985

Page: 358

View: 846

The history of physics and astronomy from the Renaissance to the present day is traced in this collection of more than one hundred and fifty entries about key scientists, concepts, discoveries, technological innovations, and learned institutions.

Stability and Chaos in Celestial Mechanics

This overview of classical celestial mechanics focuses the interplay with dynamical systems.

Stability and Chaos in Celestial Mechanics

Author: Alessandra Celletti

Publisher: Springer Science & Business Media

ISBN: 3540851461

Page: 264

View: 351

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.

Predictability Stability and Chaos in N Body Dynamical Systems

The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d'Ampezzo, Italy between August 6 and August 17, 1990 under the title "Predictability, Stability, and Chaos in N-Body Dynamical Systems ...

Predictability  Stability  and Chaos in N Body Dynamical Systems

Author: Archie E. Roy

Publisher: Springer Science & Business Media

ISBN: 146845997X

Page: 616

View: 654

The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d'Ampezzo, Italy between August 6 and August 17, 1990 under the title "Predictability, Stability, and Chaos in N-Body Dynamical Systems". The Institute was the latest in a series held at three-yearly inter vals from 1972 to 1987 in dynamical astronomy, theoretical mechanics and celestial mechanics. These previous institutes, held in high esteem by the international community of research workers, have resulted in a series of well-received Proceedings. The 1990 Institute attracted 74 participants from 16 countries, six outside the NATO group. Fifteen series of lectures were given by invited speakers; additionally some 40 valuable presentations were made by the younger participants, most of which are included in these Proceedings. The last twenty years in particular has been a time of increasingly rapid progress in tackling long-standing and also newly-arising problems in dynamics of N-body systems, point-mass and non-point-mass, a rate of progress achieved because of correspondingly rapid developments of new computer hardware and software together with the advent of new analytical techniques. It was a time of exciting progress culminating in the ability to carry out research programmes into the evolution of the outer Solar 8 System over periods of more than 10 years and to study star cluster and galactic models in unprecedented detail.

Chaos

BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations.

Chaos

Author: Kathleen Alligood

Publisher: Springer

ISBN: 3642592813

Page: 603

View: 283

BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.

Popular Astronomy

The “ chaos ” of the Greeks — the rude and formless materials , subject to no law
, out of which all things were formed by the creative power - corresponds in a
striking manner to the nebulous masses of modern astronomy . These old ideas
of ...

Popular Astronomy

Author: Simon Newcomb

Publisher:

ISBN:

Page: 566

View: 207

Chaos Resonance and Collective Dynamical Phenomena in the Solar System

DYNAMICS OF THE ZODIACAL CLOUD S. F. DERMOTT Department of
Astronomy, University of Florida, Gainesville, FL 3S611, USA H. S. GOMhlS
Observatorio National, Departamento de Astronomia, Rio de Janeiro, Brazil D. D.
DUKDA.

Chaos  Resonance and Collective Dynamical Phenomena in the Solar System

Author: Sylvio Ferraz-Mello

Publisher: Springer Science & Business Media

ISBN: 9780792317821

Page: 432

View: 640

This symposium was devoted to a new celestial mechanics whose aim has become the study of such `objects' as the planetary system, planetary rings, the asteroidal belt, meteor swarms, satellite systems, comet families, the zodiacal cloud, the preplanetary nebula, etc. When the three-body problem is considered instead of individual orbits we are, now, looking for the topology of extended regions of its phase space. This Symposium was one step in the effort to close the ties between two scientific families: the observationally-oriented scientists and the theoretically-oriented scientists.

Deep Simplicity

As profound as it is provocative, "Deep Simplicity takes us to the brink of understanding life itself.

Deep Simplicity

Author: John R. Gribbin

Publisher: Random House Incorporated

ISBN: 140006256X

Page: 275

View: 639

An astrophysicist presents a lucid, accessible explanation of the fundamental principles of chaos and complexity theory, incorporating the latest research with frequent analogies and examples to explore simple applications of the theory in everyday life. By the author of In Search of Schrödinger's Cat and The Scientists. 22,000 first printing.