Synopses & Reviews
The study of orbits in dynamical systems and the theory of order and chaos has progressed enormously over the last few decades. It thus became an essential tool in dynamical astronomy. The book is 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. This book, addressing especially the astrophysics, is also written as a textbook on dynamical systems for students in physics.
Review
From the reviews: "This excellent book should certainly find a good place in every library of research centres in astronomy and cosmology." (Physicalia, 25/3, 2003) "There is plenty of interesting and useful information in the book. [...] I was always puzzled as to why Lyapunov exponents of chaotic orbits take so long to converge, and now I understand." (Prasenjit Saha, Physics Today, Nov. 2003) "This book is the first to provide a general overview of order and chaos in this field of research.[...] This book, addressing especially astrophysicists, can also be used as a textbook on dynamical systems and astronomy for students in physics." (Zentralblatt MATH 2004, vol. 1041, page 69) "This book represents a collection of the experience accumulated by Contopoulos in about 50 years of activity. ... Researchers in dynamical systems and in astronomy and astrophysics will find in this book excellent source of information ... . Advanced students working in dynamical systems may use it as a complete textbook ... . Students in dynamical astronomy will appreciate in particular the two sections devoted to the dynamics of galaxies and to other astronomical applications." (A. Giorgilli, Mathematical Reviews, 2004 f) "The study of orbits in nonlinear dynamical systems has progressed enormously over the last decades and thus became an important tool in dynamical astronomy. ... This book is the first to provide a general overview of order and chaos in this field of research. ... Quite useful and interesting is a list of more than seventy open problems ... . This book, addressing especially astrophysicists, can also be used as a text book on dynamical systems and astronomy for students in physics." (Klaus Brod, Zentralblatt MATH, Vol. 1041 (16), 2004) "The author is a well-known scientist who has been involved in research in Dynamical Astronomy and Dynamics of galaxies for the last 50 years. ... The amount of work done is impressive, and the present Volume can be considered as a summary of ideas and numerical results obtained by the authors and collaborators. ... The book can be interesting as a source of information for the heuristic discussions following the presentation of several concrete problems in Astronomy." (Carles Simó, SIAM DS Web, January, 2004) "If you are charmed by the order-chaos dichotomy, you will find much to enjoy in the book. ... George Contopoulos has a half-century record of working on unusual but interesting problems. ... It is interesting to have a pioneer's view. ... there is plenty of interesting and useful information in the book. ... I was always puzzled as to why Lyapunov exponents of chaotic orbits take so long to converge, and now I understand." (Prasenjit Sinha, Physics Today, November, 2003) "This large monograph, more than 600 pages, is devoted to the modern approach of dynamical astronomy. ... The author, who has largely contributed to the dynamical astronomy, gives here a complete panorama of this domain in a clear and modern presentation. Mathematical concepts of the theory are nicely presented with more than 350 figures in view to make things understandable. ... This excellent book should certainly find a good place in every library of research centre in astronomy and cosmology." (Stéphane Métens, Physicalia, Vol. 25 (3), 2003) "This comprehensive book covers many important topics of dynamical systems with application to the contemporary understanding of stellar and galaxy structure and evolution. ... It should be regarded as not only a good introduction to the complicated field of dynamical astronomy, but also as a handbook for many people working in different branches of contemporary physics and astrophysics. It, therefore, will be useful for many professionals and especially postgraduate university students ... as well as for those specialized in mechanics and general dynamics." (A. M. Fridman and M. Ya. Marov, Solar System Research, Vol. 42 (3), 2008)
Review
From the reviews:
"This excellent book should certainly find a good place in every library of research centres in astronomy and cosmology." (Physicalia, 25/3, 2003)
"There is plenty of interesting and useful information in the book. [...] I was always puzzled as to why Lyapunov exponents of chaotic orbits take so long to converge, and now I understand." (Prasenjit Saha, Physics Today, Nov. 2003)
"This book is the first to provide a general overview of order and chaos in this field of research.[...] This book, addressing especially astrophysicists, can also be used as a textbook on dynamical systems and astronomy for students in physics." (Zentralblatt MATH 2004, vol. 1041, page 69)
"This book represents a collection of the experience accumulated by Contopoulos in about 50 years of activity. ... Researchers in dynamical systems and in astronomy and astrophysics will find in this book excellent source of information ... . Advanced students working in dynamical systems may use it as a complete textbook ... . Students in dynamical astronomy will appreciate in particular the two sections devoted to the dynamics of galaxies and to other astronomical applications." (A. Giorgilli, Mathematical Reviews, 2004 f)
"The study of orbits in nonlinear dynamical systems has progressed enormously over the last decades and thus became an important tool in dynamical astronomy. ... This book is the first to provide a general overview of order and chaos in this field of research. ... Quite useful and interesting is a list of more than seventy open problems ... . This book, addressing especially astrophysicists, can also be used as a text book on dynamical systems and astronomy for students in physics." (Klaus Brod, Zentralblatt MATH, Vol. 1041 (16), 2004)
"The author is a well-known scientist who has been involved in research in Dynamical Astronomy and Dynamics of galaxies for the last 50 years. ... The amount of work done is impressive, and the present Volume can be considered as a summary of ideas and numerical results obtained by the authors and collaborators. ... The book can be interesting as a source of information for the heuristic discussions following the presentation of several concrete problems in Astronomy." (Carles Simó, SIAM DS Web, January, 2004)
"If you are charmed by the order-chaos dichotomy, you will find much to enjoy in the book. ... George Contopoulos has a half-century record of working on unusual but interesting problems. ... It is interesting to have a pioneer's view. ... there is plenty of interesting and useful information in the book. ... I was always puzzled as to why Lyapunov exponents of chaotic orbits take so long to converge, and now I understand." (Prasenjit Sinha, Physics Today, November, 2003)
"This large monograph, more than 600 pages, is devoted to the modern approach of dynamical astronomy. ... The author, who has largely contributed to the dynamical astronomy, gives here a complete panorama of this domain in a clear and modern presentation. Mathematical concepts of the theory are nicely presented with more than 350 figures in view to make things understandable. ... This excellent book should certainly find a good place in every library of research centre in astronomy and cosmology." (Stéphane Métens, Physicalia, Vol. 25 (3), 2003)
"This comprehensive book covers many important topics of dynamical systems with application to the contemporary understanding of stellar and galaxy structure and evolution. ... It should be regarded as not only a good introduction to the complicated field of dynamical astronomy, but also as a handbook for many people working in different branches of contemporary physics and astrophysics. It, therefore, will be useful for many professionals and especially postgraduate university students ... as well as for those specialized in mechanics and general dynamics." (A. M. Fridman and M. Ya. Marov, Solar System Research, Vol. 42 (3), 2008)
Synopsis
There have been many books on Dynamical Astronomy up to now. Many are devoted to Celestial Mechanics, but there are also several books on Stellar and Galactic Dynamics. The first books on stellar dynamics dealt mainly with the statistics of stellar motions (e. g. Smart's "Stellar Dynamics" (1938), or Trumpler and Weaver's "Statistical Astronomy" (1953)). A classical book in this field is Chandrasekhar's "Principles of Stellar Dynamics" (1942) that dealt mainly with the time of relaxation, the solutions of Liouville's equation, and the dynamics of clusters. In the Dover edition of this book (1960) an extended Appendix was added, containing the statistical mechanics of stellar systems, a quite "modern" subject at that time. The need for a classroom book was covered for several years by the book of Mihalas and Routly "Galactic Astronomy" (1969). But the most complete book in this field is Binney and Tremaine's "Galactic Dynamics" (1987). This book covers well the classical topics of stellar dynamics, and many subjects of current interest. Another classical book in dynamical astronomy is the extensive 4-Volume treatise of Hagihara "Celestial Mechanics" (1970, 1972, 1974, 1975). In more recent years much progress has been made on new topics that are of vital interest for stellar and galactic dynamics. The main new topic is Chaos. The progress of the theory of chaos has influenced considerably the area of stellar and galactic dynamics. The study of order and chaos has provided a new dimension in dynamics.
Synopsis
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.
Table of Contents
From the contents: Historical Introduction.- Order and Chaos in General.- Terminology and Classification of Dynamical Systems.- Integrable Systems.- Third Integral.- Periodic Orbits.- Systems of Two Degrees of Freedom.- Transition from Order to Chaos.- The Last KAM Torus.- Large Perturbations.- Systems with Escapes.- Dynamical Spectra.- Systems of Three Degrees of Freedom.- Systems of N-Degrees of Freedom.- Fractals.- Order and Chaos in Galaxies.- Orbits in the Plane of Symmetry of a Galaxy.- Orbits in 3-D Galaxies.- Theoretical Orbits in Galaxies.- Self-Consistent Models.- N-Body Systems.- Dynamical Spectra of Galaxies.- Other Applications in Dynamical Astronomy.- Order and Chaos in the Solar System.- Relativistic Chaos.- Chaotic Cosmology.- Appendix A: A Particular Application of the Painleve Test.- Appendix B: Construction of an Integrable System with Higher Order Islands.- References.- Index.