TY  - BOOK
AU  - Cordani,Bruno
ED  - SpringerLink (Online service)
TI  - Geography of Order and Chaos in Mechanics: Investigations of Quasi-Integrable Systems with Analytical, Numerical, and Graphical Tools 
T2  - Progress in Mathematical Physics
SN  - 9780817683702
AV  - QA401-425 
U1  - 530.15 23
PY  - 2013///
CY  - New York, NY
PB  - Springer New York, Imprint: Birkhäuser
KW  - Mathematics
KW  - Partial differential equations
KW  - Differential geometry
KW  - Mathematical physics
KW  - Physics
KW  - Statistical physics
KW  - Mathematical Physics
KW  - Differential Geometry
KW  - Nonlinear Dynamics
KW  - Partial Differential Equations
KW  - Numerical and Computational Physics
KW  - Mathematical Methods in Physics
N1  - Preface -- List of Figures -- 1 Introductory Survey -- 2 Analytical Mechanics and Integrable Systems -- 3 Perturbation Theory -- 4 Numerical Tools I: ODE Integration -- 5 Numerical Tools II: Detecting Order, Chaos, and Resonances -- 6 The Kepler Problem -- 7 The KEPLER Program -- 8 Some Perturbed Keplerian Systems -- 9 The Multi-Body Gravitational Problem -- Bibliography -- Index
N2  - This original monograph aims to explore the dynamics in the particular but very important and significant case of quasi-integrable Hamiltonian systems, or integrable systems slightly perturbed by other forces. With both analytic and numerical methods, the book studies several of these systems—including for example the hydrogen atom or the solar system, with the associated Arnold web—through modern tools such as the frequency-modified fourier transform, wavelets, and the frequency-modulation indicator. Meanwhile, it draws heavily on the more standard KAM and Nekhoroshev theorems. Geography of Order and Chaos in Mechanics contains many figures that illuminate its concepts in novel ways, but perhaps its most useful feature is its inclusion of software to reproduce the various numerical experiments. The graphical user interfaces of five supplied MATLAB programs allows readers without any knowledge of computer programming to visualize and experiment with the distribution of order, chaos and resonances in various Hamiltonian systems. This monograph will be a valuable resource for professional researchers and certain advanced undergraduate students in mathematics and physics, but mostly will be an exceptional reference for Ph.D. students with an interest in perturbation theory
UR  - http://dx.doi.org/10.1007/978-0-8176-8370-2
ER  -