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Abdullaev S.S. — Construction of Mappings for Hamiltonian Systems and Their Applications
Abdullaev S.S. — Construction of Mappings  for Hamiltonian Systems  and Their Applications

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Название: Construction of Mappings for Hamiltonian Systems and Their Applications

Автор: Abdullaev S.S.

Аннотация:

Based on the method of canonical transformation of variables and the classical perturbation theory, this innovative book treats the systematic theory of symplectic mappings for Hamiltonian systems and its application to the study of the dynamics and chaos of various physical problems described by Hamiltonian systems. It develops a new, mathematically-rigorous method to construct symplectic mappings which replaces the dynamics of continuous Hamiltonian systems by the discrete ones. Applications of the mapping methods encompass the chaos theory in non-twist and non-smooth dynamical systems, the structure and chaotic transport in the stochastic layer, the magnetic field lines in magnetically confinement devices of plasmas, ray dynamics in waveguides, etc. The book is intended for postgraduate students and researches, physicists and astronomers working in the areas of plasma physics, hydrodynamics, celestial mechanics, dynamical astronomy, and accelerator physics. It should also be useful for applied mathematicians involved in analytical and numerical studies of dynamical systems.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 378

Добавлена в каталог: 09.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Action-angle variables      8
Action-angle variables, many degrees of freedom      9
Action-angle variables, one degree of freedom      9
Aphelion      132
Arnold diffusion      149
Aspect ratio      224
Averaging principle      21 22
Backward map      282
Betatron oscillations      310
Chaos      145
Chaos, global      149
Chirikov criteria      149
Clebsch representation      221
Correlation function      198
Correlation time      198
Devil's staircase      306
Diffusion coefficient      200
Diffusion coefficient, field lines      265
Diffusion coefficient, global      265
Diffusion coefficient, local      265
Diffusion coefficient, quasilinear      200 266
Diffusion process      201
Diffusion process, normal      201
Diffusion process, sub diffusive      201
Diffusion process, superdiffusive      201
Dynamical aperture      308
Dynamical entropy      199
Eikonal equation      301
Elliptic fixed points      12
Ergodic divertor      255
Ergodic motion      197
Ergodic zone      255
Fermat's principle      299
Fermi acceleration mapping      49
Forward map      282
Fundamental problem of dynamics      22
Generating function      5
Generating function, Lie      26
Generating function, mixed variable      26
Hamilton — Jacobi equation      6
Hamilton — Jacobi equation, complete integral      6
Hamilton's function      1
Hamilton, equations      1
Hamiltonian      1
Heteroclinic orbit      83
High field side      257
Homoclinic orbit      83
Hyperbolic fixed points      12
Integrability      7
Integral invariants, Poincare — Cartan      3
Intermittence      166
Invariant curve      141
Invariants of motion      2
Jacobi's theorem      6
KAM theory      23 139
Kepler map      132 135 138 316
Kolmogorov entropy      199
Kolmogorov's technique      36
Laminar zone      267
Levy flight      213
Liouville theorem      7
Low field side      257
Lyapunov exponent      147
Magnetic field, equilibrium      220
Magnetic footprints      270 296
Magnetic stochasticity      230
Magnetic surfaces      220
Major radius      222
Map, Full turn transfer      310
Melnikov type integrals      94—96
Melnikov type integrals, asymptotics      321
Minor radius      224
Mixing      198
Nonlinear resonance      142
Nonlinear resonance, width      143
Nonsmooth map      168
Nontwist map      243
Nontwist standard map      158
Nontwist systems      151
Nontwist systems, condition      151
Optical length      307
Paraxial approximation      301
Pendulum      12
Perihelion      132
Perturbation series      23
Perturbation series, Lindstedt method      23
Perturbation theory      21
Poincare map      39
Poincare recurrence      203
Poincare — Birkhoff theorem      142
Poloidal angle, intrinsic      220
Poloidal divertor, double-null      275
Poloidal divertor, single-null      275
Poloidal field      224
Poloidal flux      220
Primary resonant approximation      98
Quasilinear theory      200
Rescaling invariance      175
Rescaling invariance, in parameter space      182
Rescaling invariance, proof      179
Rescaling invariance, universal      178
Rescaling parameter      118 175 178
Residence time      202
Revtokamap      243
Safety factor      221
Separatrix      13 83
Separatrix map      83 85 86
Separatrix map, algorithmic      112
Separatrix, magnetic      275 278
Shafranov shift      226
Shear less curve      151
Smooth perturbations      150 173
Smoothness parameter      150
Splitting of separatrices      144
Stable and unstable manifolds      144
Standard magnetic field      224
Standard map      47 69 241
Standard map, symmetric      69
Stellarator      219
Stochastic layer      83 84
Stochastic web      165
Stroboscopic map      39
Symmetric map      56
Symplectic correctors      47
Symplectic integration      17
Symplectic map      3
Synchrotron oscillations      310
Taylor map      311
Tokamak      219
Tokamak divertor maps      277
Tokamak, Poloidal divertor      275
Tokamap      242
Tokamap, symmetric      247
Toroidal angle      220
Toroidal field      224
Toroidal flux      220
Torus      7
Torus, non-resonant      139
Torus, resonant      140
Tracking      310
Twist condition      43 140
Twist map, perturbed      43 55
Twist map, radial      46
Twist map, symmetric      67
Volume-preserving map      3
Weak chaos      165
Whisker map      83 85 86
Winding number      221
X-point      275
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