Stable and Random Motions in Dynamical Systems
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A01=Jurgen Moser
Accuracy and precision
Action-angle coordinates
Analytic function
Author_Jurgen Moser
Bounded variation
Category=PBKJ
Category=PHVB
Chaos theory
Coefficient
Constant term
Continuous embedding
Continuous function
Coordinate system
Degrees of freedom
Degrees of freedom (statistics)
Derivative
Differentiable function
Differential equation
Dimension (vector space)
Discrete group
Divisor
Duffing equation
Eigenfunction
Eigenvalues and eigenvectors
Energy level
eq_bestseller
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
eq_science
Equation
Ergodic theory
Ergodicity
Existence theorem
First-order partial differential equation
Forcing function (differential equations)
Gravitational constant
Hamiltonian mechanics
Hamiltonian system
Heteroclinic orbit
Hyperbolic partial differential equation
Integrable system
Integration by parts
Invariant manifold
Invertible matrix
Jordan curve theorem
Linear map
Linear subspace
Linearization
Maxima and minima
Monotonic function
Newton's method
Normal bundle
Partial differential equation
Periodic function
Periodic point
Perturbation theory (quantum mechanics)
Phase space
Polynomial
Probability theory
Quasiperiodic motion
Rate of convergence
Rational dependence
Regular element
Root of unity
Smoothness
Special case
Stability theory
Statistical mechanics
Structural stability
Symbolic dynamics
Symmetric matrix
Tangent space
Theorem
Uniqueness theorem
Unitary matrix
Variational principle
Vector field
Product details
- ISBN 9780691089102
- Weight: 340g
- Dimensions: 152 x 235mm
- Publication Date: 06 May 2001
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jurgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis.
After thirty years, Moser's lectures are still one of the best entrees to the fascinating worlds of order and chaos in dynamics.
Daniel M. Kammen is Associate Professor of Energy and Society and director of the Renewable and Appropriate Energy Laboratory at the University of California, Berkeley. David M. Hassenzahl is Assistant Professor of Environmental Studies at the University of Nevada, Las Vegas. He has been an environmental risk professional in both the public and private sectors. Jurgen Moser, who died in 1999, was one of the most influential mathematicians of his generation. He made key contributions in dynamical systems and nonlinear analysis and was Director of the NYU Courant Institute, Director of the Research Institute for Mathematics at Switzerland's Federal Institute of Technology, and President of the International Mathematical Union. He received the 1994/95 Wolf Prize.
