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Kunze M. — Non-Smooth Dynamical Systems
Kunze M. — Non-Smooth Dynamical Systems

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Название: Non-Smooth Dynamical Systems

Автор: Kunze M.

Аннотация:

The book provides a self-contained introduction to the mathematical theory of non-smooth dynamical problems, as they frequently arise from mechanical systems with friction and/or impacts. It is aimed at applied mathematicians, engineers, and applied scientists in general who wish to learn the subject.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 228

Добавлена в каталог: 18.08.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\varepsilon-\delta$-usc      8
Absolutely continuous function      12
Action-angle variables      164 167 171
Addition Property      146 152
Almost periodic function      58
Arzela — Ascoli theorem      15
Assumption (A1)      71
Assumption (A10)      86
Assumption (A2)      71
Assumption (A3)      71
Assumption (A4)      71
Assumption (A5)      71
Assumption (A6)      71
Assumption (A7)      71
Assumption (A8)      71
Assumption (A9)      79
Basic assumptions (I)      147
Basic assumptions (II)      154
Bifurcation point      158
Billiards      206
Bouncing ball problems      205
Burridge — Knopoff model      203
Cocycle      63 136
Conley index applications      158
Conley index for multi-valued maps      150
Conley index introduction      143
Conservative problems, boundedness of solutions      165
Conservative problems, periodic solutions      41
Conservative problems, unbounded solutions      23
Constant type irrational      175
Continuation theorem      146 157
Differential inclusions, definition of solutions      12
Differential inclusions, existence of solutions      13
Differential inclusions, numerical simulations      203
Differential inclusions, uniqueness of solutions      16
Differentiation of chain functions      177
Ergodic measure      135
Existence principle      147 152
Fermi accelerator problem      205
Fixed point of multi-valued mapping      11
Function, absolutely continuous      12
Function, almost periodic      58
Generalized polar coordinates      189
Graze      206
Grazing bifurcations      206
Hilbert's 16th problem      185
Hopf bifurcation      192
Impact oscillator      204
Integrability conditions      64 84 85 136
Intersection property      177
Invariant curve theorem      see "Twist theorem"
Invariant measure      135
Isolated invariant set      144 149
Isolating block      145
Isolating neighborhood      143 149
Lienard equation      191
Linear complementarity problems (LCPs)      209
Lyapunov constant      187
Lyapunov exponents, definition      64 136
Lyapunov exponents, numerical evaluation      203
Lyapunov exponents, upper      63 118
Markoff constant      175
Measure, ergodic      135
Measure, invariant      135
Melnikov's method      197
Multi-body systems      207
Multi-valued differential equations      see "Differential inclusions"
Multi-valued mapping      7
Oseledets' multiplicative ergodic theorem      64 136
Pendulum with dry friction, almost periodic solutions      46
Pendulum with dry friction, boundedness of solutions      26
Pendulum with dry friction, integrability conditions      125
Pendulum with dry friction, more general friction laws      39 209
Pendulum with dry friction, non-positivity of Lyapunov exponents      119
Pendulum with dry friction, periodic solutions      33
Pendulum with dry friction, resonant case      117 129
Pendulum with dry friction, small amplitude case      113 127
Pendulum with dry friction, unbounded solutions      23
Piecewise linear planar      195
Poincare — Bendixson theorem      191
Principle of linearized stability      39
Rocking block system      203
Schauder's fixed point theorem      11
Selection      7
Singularity of focus-focus type      185
State-dependent coefficient of friction      39
State-dependent stiffness      205
Tangent cone      9
Theorem, Arzela — Ascoli      15
Theorem, continuation      146 157
Theorem, invariant curve      168 176
Theorem, Oseledets' multiplicative ergodic      64 136
Theorem, Poincare — Bendixson      191
Theorem, Schauder's fixed point      11
Theorem, twist      168 176
Twist theorem formulation      168 176
Twist theorem introduction      166
Uniformly (un-) bounded w.r. to initial values and phases      111
Upper Lyapunov exponents      63 118
Usc      8
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