At a Glance
624 Pages
23.5 x 15.5 x 3.51
Hardcover
$176.90
Aims to ship in 7 to 10 business days
Industry Reviews
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 isimpressive, 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 Simo, 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." (Stephane Metens, 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)
Historical Introduction | p. 1 |
Celestial Mechanics | p. 1 |
Statistical Mechanics | p. 2 |
Dynamical Astronomy | p. 3 |
Computer Experiments | p. 4 |
The Third Integral | p. 5 |
Order and Chaos | p. 6 |
Applications to Galaxies | p. 8 |
Other applications | p. 9 |
Order and Chaos in General | p. 11 |
Terminology and Classification | p. 11 |
Dynamical Systems | p. 11 |
Integrable, Chaotic, Ergodic, Mixing, Kolmogorov and Anosov Systems | p. 13 |
Old and New Classification | p. 17 |
Integrable Systems | p. 20 |
Examples of Integrable Systems | p. 20 |
Separable Systems | p. 25 |
Time Dependent Systems | p. 27 |
Integrals in Velocity-Dependent Potentials and in Maps | p. 29 |
Stäckel Potentials in 2 Dimensions | p. 30 |
A Rotating Stäckel Model | p. 36 |
Stäckel Potentials in 3 Dimensions | p. 37 |
The Toda Lattice | p. 42 |
Painlevé Analysis | p. 46 |
Check of Integrability | p. 48 |
The Third Integral | p. 49 |
Formal Integrals | p. 49 |
Resonance Cases | p. 54 |
Construction of the Integrals and of the Normal Forms | p. 58 |
The Problem of Convergence | p. 62 |
KAM Theory | p. 67 |
Nekhoroshev Theory | p. 71 |
Superexponential Stability | p. 74 |
Destruction of the Integrals | p. 75 |
The Third Integral in Periodic Potentials | p. 78 |
Adiabatic Invariants | p. 82 |
Other Types of Integrals | p. 86 |
Rational Solutions. The Prendergast Method | p. 88 |
The Averaging Method | p. 92 |
Periodic Orbits | p. 93 |
Surfaces of Section | p. 93 |
Stable and Unstable Periodic Orbits | p. 97 |
Bifurcations | p. 101 |
Characteristics | p. 106 |
The Poincaré-Birkhoff Theorem | p. 111 |
Theoretical Computation of Periodic Orbits | p. 115 |
Systems of Two Degrees of Freedom | p. 122 |
Forms of the Orbits | p. 122 |
Invariant Curves | p. 126 |
Chaotic Orbits | p. 129 |
Resonant Islands | p. 133 |
Rotation Numbers | p. 139 |
Asymptotic Curves and Homoclinic Points | p. 144 |
Smale Horseshoes | p. 151 |
Poincaré Recurrence | p. 154 |
Distribution of Periodic Orbits | p. 158 |
Transition from Order to Chaos | p. 168 |
The Logistic Map | p. 168 |
Dissipative and Conservative Systems | p. 173 |
Routes to Chaos | p. 180 |
Resonance Overlap | p. 185 |
The Last KAM Torus | p. 192 |
Properties of the last KAM torus | p. 192 |
Methods for Locating the Last KAM Torus | p. 196 |
Cantori and Stickiness | p. 203 |
Destruction of the Islands of Stability | p. 213 |
Large Perturbations | p. 220 |
Heteroclinic Points | p. 220 |
Systems without Escapes | p. 222 |
The Anisotropic Kepler Problem | p. 227 |
Converse KAM Theory and the Anti-Integrability Limit | p. 227 |
Normal Diffusion and Anomalous Diffusion | p. 228 |
Linear Ergodic Systems | p. 233 |
Systems with Escapes | p. 237 |
Transition to Escape | p. 237 |
Basins of Escape and Escape Times | p. 244 |
Chaotic Scattering | p. 248 |
Dynamical Spectra | p. 251 |
Lyapunov Characteristic Numbers | p. 251 |
Spectra of Stretching Numbers | p. 257 |
Angular Spectra | p. 262 |
Explanation of the Forms of the Spectra | p. 265 |
Distinction Between Ordered and Chaotic Motions | p. 270 |
Frequency Analysis | p. 274 |
Comparison of Various Methods | p. 277 |
Spectra of Linear Systems | p. 280 |
Chaos vs. Randomness and Noise | p. 280 |
Accuracy of Numerical Orbits. Shadowing | p. 283 |
Systems of Three Degrees of Freedom | p. 284 |
Periodic Orbits and Stability Types | p. 284 |
Bifurcations and their Collisions | p. 290 |
The Kiein-Moser Theorem | p. 298 |
Simple Resonant 3-D Systems | p. 300 |
Qualitative Changes in 3-D Systems | p. 304 |
Complex Instability | p. 308 |
Termination of Sequences of Bifurcations | p. 315 |
Distribution of Periodic Orbits | p. 318 |
Periodic and Nonperiodic Orbits Derived Theoretically | p. 322 |
Ordered and Chaotic Domains | p. 327 |
4-D Surfaces of Section | p. 332 |
Nonperiodic Orbits in 4-D Maps | p. 335 |
Spectra of 4-D Maps | p. 339 |
Arnold Diffusion | p. 344 |
Systems of N Degrees of Freedom | p. 351 |
The Fermi-Pasta-Ulam Problem | p. 351 |
N-Body Chains | p. 354 |
Resonant and Nonresonant Modes | p. 358 |
A Classical Planck Spectrum | p. 360 |
Lyapunov Characteristic Numbers and Spectra of N-Body Systems | p. 362 |
Solitons in Discrete Systems | p. 364 |
Geodesic Flows | p. 366 |
Fractals | p. 369 |
Simple Fractals | p. 369 |
Generalized Dimensions | p. 373 |
Multifractals | p. 375 |
Order and Chaos in Galaxies | p. 377 |
Orbits in 2-D Galaxies | p. 377 |
Types of Orbits. The Main Resonances | p. 377 |
Epicyclic Orbits | p. 381 |
Axisymmetric and Nonaxisymmetric Models | p. 385 |
The Main Families of Periodic Orbits | p. 390 |
Short and Long Period Orbits | p. 404 |
Nonperiodic Orbits | p. 410 |
Rings, Shocks and Vortices | p. 416 |
Locating Corotation | p. 419 |
Escaping Orbits | p. 420 |
Orbits in 3-D Galaxies | p. 422 |
The Main Families of Orbits | p. 422 |
Polar Rings | p. 426 |
Warped and Buckled Galaxies | p. 428 |
Peanut and Box Galaxies | p. 430 |
Chaotic Orbits in Galaxies | p. 432 |
Theoretical Orbits in Galaxies | p. 433 |
Integrable and Nonintegrable Galactic Models | p. 433 |
Third Integral in the Meridian Plane | p. 434 |
Third Integral in Spiral and Barred Galaxies | p. 436 |
Integrals near Corotation | p. 447 |
Theoretical Explanation of the Bifurcations and Gaps | p. 455 |
The Nonlinear Density Wave Theory | p. 461 |
The Response Density | p. 467 |
Termination of Bars and Spirals | p. 473 |
Preference of Trailing Waves | p. 477 |
Third Integrals in N-Body Systems | p. 479 |
Orbits in Periodic Potentials | p. 486 |
Orbits in Evolving Galaxies | p. 489 |
Self-Consistent Models | p. 490 |
Analytical Methods | p. 490 |
The Schwarzschild Method and its Variants | p. 492 |
Self-Consistent Models of Elliptical Galaxies | p. 494 |
Self-Consistent Models of Spiral Galaxies | p. 497 |
Self-Consistent Models of Barred Galaxies | p. 502 |
N-Body Systems | p. 503 |
Methods of N-Body Simulations | p. 503 |
Collisional and Collisionless Relaxation | p. 506 |
Violent Relaxation and Lynden-Bell Statistics | p. 513 |
Distribution Functions for Spherical N-Body Systems | p. 516 |
Memory of Initial Conditions | p. 518 |
Counterrotating Galaxies | p. 520 |
A One-Dimensional Gravitational Gas | p. 521 |
Gravothermal Catastrophe | p. 524 |
Global Dynamics of Galaxies | p. 527 |
Dynamical Spectra of Galaxies | p. 529 |
Dynamical Spectra of Hamiltonian Systems | p. 529 |
Dynamical Spectra of Oscillating Galaxies | p. 533 |
Frequency Analysis in Galaxies | p. 535 |
Other Applications in Dynamical Astronomy | p. 539 |
Order and Chaos in the Solar System | p. 539 |
Order and Chaos in the Restricted Three-Body Problem | p. 539 |
The Trojan Asteroids | p. 543 |
The Sitnikov Problem | p. 544 |
The General Three Body Problem. Collisions | p. 546 |
Chaos in the Solar System | p. 549 |
Gaps in the Distribution of Asteroids | p. 552 |
Stable Chaos | p. 554 |
Lyapunov Time and Macroscopic Instability Time | p. 555 |
Relativistic Chaos | p. 556 |
Chaos in the Case ofTwo Fixed Black Holes | p. 556 |
Comparison with the Classical Theory | p. 564 |
Chaos in Various Relativistic Problems | p. 567 |
Chaotic Cosmology | p. 568 |
The Mixmaster Cosmology | p. 568 |
The Nonintegrability of the Mixmaster Model | p. 569 |
Chaos and Order in Other Cosmological Models | p. 572 |
Appendix A | p. 575 |
Appendix B | p. 579 |
Some Open Problems | p. 583 |
References | p. 587 |
Index | p. 619 |
Table of Contents provided by Publisher. All Rights Reserved. |
ISBN: 9783540433606
ISBN-10: 3540433600
Series: Astronomy and Astrophysics Library
Published: 16th June 2004
Format: Hardcover
Language: English
Number of Pages: 624
Audience: Professional and Scholarly
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5 x 3.51
Weight (kg): 1.05
Shipping
Standard Shipping | Express Shipping | |
---|---|---|
Metro postcodes: | $9.99 | $14.95 |
Regional postcodes: | $9.99 | $14.95 |
Rural postcodes: | $9.99 | $14.95 |
How to return your order
At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.
Additional postage charges may be applicable.
Defective items
If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.
For more info please visit our Help Centre.