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Broer H.W., Huitema G.B. — Quasi-Periodic Motions in Families of Dynamical Systems, Vol. 164
Broer H.W., Huitema G.B. — Quasi-Periodic Motions in Families of Dynamical Systems, Vol. 164



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Название: Quasi-Periodic Motions in Families of Dynamical Systems, Vol. 164

Авторы: Broer H.W., Huitema G.B.

Аннотация:

This book is on Kolmogorov-Arnol'd-Moser theory for quasi-periodic tori in dynamical systems. It gives an up-to-date report on the role parameters play for persis- tence of such tori, typically occuring on Cantor sets of positive Hausdorff measure inside phase and parameter space. The cases with preservation of symplectic or volume forms or time-reversal symmetries are included. The concepts of Whitney-smoothness and Diophantine approximation of Cantor sets on submanifolds of Euclidean space are treated, as well as Bruno's theory on analytic continuation of tori. Partly this material is new to Western mathematicians. The reader should be familiar with dynamical systems theory, differen- tial equations and some analysis. The book is directed to researchers, but its entrance level is introductory.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 195

Добавлена в каталог: 03.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Action-angle variables      20
Anisotropic differentiability      39
Approximation function      39
Approximation Lemma      157
Arnol’d determinant      110
Arnol’d diffusion      110
Arnol’d — Moser theorem      137
Aubry — Mather set      113
Bakhtin lemma      167
Birkhoff normal form      89
Birkhoff normal form, partial      89 90
Bochner theorem      21
Bruno condition $\beta$      164
Bruno matrix      164
Bruno normal form      163
Bruno seminormai form      163
Bruno theory      78 161
Cantor set      11 36
Cantor — Bendixson Theorem      11 36
Cantorus      113
Cauchy estimate      147
Characteristic multiplier      4
Chebyshev polynomials      167
Circle map      9
Compact-open topology      143
Conditionally periodic dynamics      2 123
Conjugacy      10
context      1
Context, dissipative      5 21 124
Context, Hamiltonian      5 18
Context, Hamiltonian, coisotropic      25
Context, Hamiltonian, isotropic      23
Context, reversible      6 20 26 125
Context, reversible, reversible 1      27
Context, reversible, reversible 2      27 28
Context, symplectic      124
Context, symplectic, coisotropic      125
Context, symplectic, isotropic      124
Context, symplectic, volume preserving      5 18 22 124
Coupling Lemma      114
Darboux theorem, generalized      23
Diffeomorphism, $C^{\infty}$-near-the-identity      154
Diffeomorphism, area preserving      14
Diffeomorphism, exact symplectic      125
Diffeomorphism, globally volume preserving      124
Diffeomorphism, r-exact symplectic      125
Diffeomorphism, reversible      125
Diffeomorphism, symplectic      125
Diffeomorphism, vertical      9
Diffeomorphism, volume preserving      124
Differential form, nondegenerate      158
Diophantine approximation lemma      62 165
Diophantine approximations      35
Diophantine approximations of dependent quantities      61
Elliptic normal modes      83
Elliptic normal modes, excitation of      84
EQUIVALENCE      8
Extension operator      156
Floquet matrix      4 124
Floquet multiplier      4
Frequencies, internal      2 46 123
Frequencies, normal      4 46 124
Hamilton function      18
Hamilton function with intrinsic degeneracy      53
Hamilton function with limit degeneracy      53
Hamilton function with proper degeneracy      53
Hamilton function, completely integrable      20
Hamilton function, convex      111
Hamilton function, integrable in the sense of Liouville      20
Hamilton function, nondegenerate in the sense of Kolmogorov      103
Hamilton function, nondegenerate in the sense of Riissmann      102
Hamilton function, nondegenerate isoenergetically      109
Hamilton function, quasi-convex      111
Hamilton function, steep      110
Hamilton function, superintegrable      53
Hausdorff measure      vii
Herman theorem      31
Holder condition      155
Holder norm      155
Homological equation      10
Hopf bifurcation      115 118
Hopf bifurcation, for cycles      119
Hopf bifurcation, quasi-periodic      115
Hopf bifurcation, quasi-periodic, skew      121
Hopf — Landau bifurcation      121
Intersection property      46 128
Invariant tori, branching off      117
Invariant tori, finitely Whitney-smooth family of      47
Invariant tori, Whitney-smooth family of      16 45
Invariant tori, Whitney-smooth family of, dressed with other tori      84
Invariant torus      2 123
Invariant torus, $\zeta$-coisotropic      159
Invariant torus, almost (nearly)      113
Invariant torus, coisotropic      19
Invariant torus, Diophantine      3 123
Invariant torus, Floquet      3 124
Invariant torus, isotropic      19
Invariant torus, Lagrangian      19
Invariant torus, lower-dimensional      53 55 128
Invariant torus, lower-dimensional, elliptic      53 55
Invariant torus, lower-dimensional, hyperbolic      53 55
Invariant torus, nonresonant      2 123
Invariant torus, periodically      130
Invariant torus, quasi-periodic      2 123
Invariant torus, resonant      2 123
Invariant torus, stickiness of      112
Invariant torus, with parallel dynamics      2 123
Invariant torus, “phase-lock”      8
Inverse Approximation Lemma      156
Involution      18
Involution, fixed point manifold of      21
Involution, functions in      19
Involution, type of      21
jet      139
KAM theory      3 11 74
KAM theory, classical      5 53
KAM theory, converse      73
KAM theory, local      90
KAM theory, multiparameter      47
KAM theory, small twist      92 108 133
KAM torus      103
Kolmogorov set      103
Kronecker cascade      123
Kronecker flow      2
Kupka — Smale theorem      8
Lebesgue density point      133
Limit cycle birth/annihilation bifurcation      118
Liouvile — Arnoi’d theorem      19
Liouville tori      20
Lipschitz condition      155
Local Hopf family      116
localization      98
Lyapunov center theorem      96
Lyapunov — Devaney theorem      96
Manifold, exact symplectic      125
Manifold, r-exact symplectic      125
Matrix, Hamiltonian      24
Matrix, infmitesimaiiy reversible      27
Matrix, infmitesimaiiy symplectic      24
Matveev theorem      139
Miniparameter theorems      61
Morbidelli — Giorgilli theorem      112
Moser modifying terms      47
Neimark excitation      119
Neimark — Sacker bifurcation      115 119
Nekhoroshev theorem      110
Newtonian iteration process      145
Normal Form Lemma      89
Normal Form Lemma, quasi-periodic      116 131
Paley — Wiener lemma      37
Parallel dynamics      2 123
Parasyuk theorem      31
Period-doubling bifurcation      115
Persistence      17
Phase oscillations      106
Poincare map for the period      14 131
Poincare return map      9 130
Poincare return map, isoenergetic      130
Poincare section      130
Poincare section, isoenergetic      130
Poincare theorem      105
Poincare trajectory      105
Poincare — Andronov bifurcation      118
Poincare — Dulac normal form      89
Poisson bracket      19
Quasi-periodic attractor      6
Quasi-periodic response      15
Reducibility problem      4 32
Relaxed theorems      55
Resonance layer      103
Resonance zone      103
Rotation number      9
Saddle-node bifurcation      115
Separatrix manifolds      78 111
Small divisors      11 34 35
Small divisors, 1-bite problem with      32
Stability exponents      110
Stability, $\Omega$-      142
Stability, effective      110
Stability, in the sense of Lyapunov      135
Stability, KAM-      17
Stability, of the action variables      110
Stability, quasi-periodic      13 47 142
Stability, structural      12
Stability, weak quasi-periodic      13
Stabilization via resonance      111
Steepness indices      110
Submanifold, $\zeta$-coisotropic      159
Submanifold, coisotropic      19
Submanifold, isotropic      19
Submanifold, Lagrangian      19
Subtorus      2 104 123
Superexponential estimates      38 112 154
Symplectic structure, r-exact      125
Thirring model      144
Treshchev theorem      107
Treshchev torus      107
Twist map      14
van der Pol oscillator      7
Variational equation      4
Variational Principle      113
Vector field, $\zeta$-preserving      159
Vector field, divergence of      18
Vector field, divergence-free      18
Vector field, generic      30
Vector field, globally $\zeta$-preserving      159
Vector field, globally divergence-free      18
Vector field, Hamiltonian      18
Vector field, Hamiltonian, quasi-ergodic      112
Vector field, integrable      17 21 48
Vector field, reversible      20
Vector field, typical      30
Vector field, vertical      16 141
Whiskers      78 111
Whitney extension theorem      156
Whitney-smooth foliation      36
Whitney-smoothness      11 36 44 155 156
Winding number      9
Zygmund condition      156
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