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Schmidt K. — Dynamical systems of algebraic origin
Schmidt K. — Dynamical systems of algebraic origin

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Название: Dynamical systems of algebraic origin

Автор: Schmidt K.

Аннотация:

Although the study of dynamical systems is mainly concerned with single transformations and one-parameter flows (i.e. with actions of Z, N, M, or M+), er-godic theory inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multi-dimensional symmetry groups. However, the wealth of concrete and natural examples, which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. A remarkable exception is provided by a class of geometric actions of (discrete subgroups of) semi-simple Lie groups, which have led to the discovery of one of the most striking new phenomena in multi-dimensional ergodic theory: under suitable circumstances orbit equivalence of such actions implies not only measurable conjugacy, but the conjugating map itself has to be extremely well behaved. Some of these rigidity properties are inherited by certain abelian subgroups of these groups, but the very special nature of the actions involved does not allow any general conjectures about actions of multi-dimensional abelian groups...


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 320

Добавлена в каталог: 23.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$0_{X}$, $1_{X}$, 0, 1      1
$1_{B}$      xvi
$a^{\blacktriangledown}$      247
$a^{\blacktriangle}$      247
$A^{\bot}$      12
$A^{\top}$      7
$a^{\triangledown}$      247
$a^{\vartriangle}$      247
$dim_{h}(\alpha)$      226
$e^{(i)}$      71
$E_{\mu}$      108
$Fix(\alpha)$      94
$Fix_{\Lambda}(\alpha)$      47
$f^{n,\blacktriangledown}$      247
$f^{n,\blacktriangle}$      247
$f^{\blacktriangledown}$      247
$f^{\blacktriangle}$      247
$f^{\triangledown}$      247
$f^{\vartriangle}$      247
$f_{\Phi}$      153
$GL(n,\mathcal{R})$      xvi
$h^{(n)}_{\mu}(T^{(\Gamma)})$      242
$h^{(n)}_{\mu}(T^{(\Gamma)},\mathcal{Q})$      242
$h_{cover}$      105
$h_{sep}$      106
$h_{span}$      106
$h_{top}$      106
$H_{\mu}$      108
$id_{X}$      1
$I_{\mu}$      108
$j_{c}$      60
$M_{1}(X)$      111
$M_{1}(X)^{T}$      111
$o_{v}$      62
$o_{\mathbb{K}}$      62
$p^{+}(\alpha)$      175
$p^{-}(\alpha)$      175
$P^{\mathbb{K}}$      62
$P^{\mathbb{K}}_{f}$      62
$P^{\mathbb{K}}_{\infty}$      62
$R_{c}$      64
$R_{F}$      63
$SL(n,\mathcal{R})$      xvi
$V_{\mathbb{C}}(a)$      44
$X^{\circ}$      1
$X_{F}$      228
$\alpha$-periodic point      39
$\alpha^{(c)}$      64
$\alpha^{(\Delta)}$      2
$\alpha^{A}$      80
$\alpha^{V}$      1
$\alpha^{X/V}$      1
$\alpha^{\mathfrak{M}}$      36
$\alpha_{A}$      143
$\alpha_{F}$      59
$\beta^{A}$      80
$\hat{\alpha}^{\mathfrak{M}}$      36
$\langle Q \rangle$      105
$\langle\Lambda\rangle$      174
$\mathbb{C}$      xvi
$\mathbb{F}_{p^{k}}$      228
$\mathbb{F}_{p}$      43
$\mathbb{K}_{A}$      62
$\mathbb{K}_{v}$      61
$\mathbb{M}(f)$      125
$\mathbb{N}$      xvi
$\mathbb{N}^{*}$      xvi
$\mathbb{Q}$      xvi
$\mathbb{Q}_{p}$      61
$\mathbb{R}$      xvi
$\mathbb{R}^{+}$      xvi
$\mathbb{S}$      xvi
$\mathbb{T}$      xvi
$\mathbb{Z}$      xvi
$\mathbb{Z}[\frac{1}{n}]$      xvi
$\mathbb{Z}[\mathbb{Z}^{d}]$      35
$\mathbb{Z}^{d}$-action, aperiodic      173
$\mathbb{Z}^{d}$-action, Bernoulli      196
$\mathbb{Z}^{d}$-action, by automorphisms      35
$\mathbb{Z}^{d}$-action, by automorphisms, almost minimal      285
$\mathbb{Z}^{d}$-action, by automorphisms, faithful      173
$\mathbb{Z}^{d}$-action, continuous      105 293
$\mathbb{Z}^{d}$-action, ergodic      47
$\mathbb{Z}^{d}$-action, expansive      114
$\mathbb{Z}^{d}$-action, mixing      8
$\mathbb{Z}^{d}$-action, n-mixing      169
$\mathbb{Z}^{d}$-action, with completely positive entropy      162
$\mathbb{Z}_{/n}$      18
$\mathbb{Z}_{p}}$      18
$\mathcal{B}_{N}$      201
$\mathcal{C}(f)$      153 270
$\mathcal{E}(f)$      270
$\mathcal{P}^{-}_{T}$      109 162
$\mathcal{P}_{0}$      222
$\mathcal{P}_{T}$      162
$\mathcal{R}^{(k)}$      290
$\mathcal{R}^{(p)}_{d}$      269
$\mathcal{R}_{v}$      62
$\mathcal{S}(f)$      144 270
$\mathfrak{A}_{T}(\mathcal{Q},n)^{-}_{t}$      242
$\mathfrak{A}_{T}(\mathcal{Q},n)_{-\infty}$      242
$\mathfrak{A}_{T}(\mathcal{Q},n)_{t}$      242
$\mathfrak{A}_{X}(\mathcal{Q})_{-\infty}$      234
$\mathfrak{A}_{X}(\mathcal{Q})_{k}$      234
$\mathfrak{B}(T)$      162
$\mathfrak{B}_{X}$      2
$\mathfrak{R}^{(p)}_{d}$      43
$\mathfrak{R}^{(p)}_{d}$-module      59
$\mathfrak{R}^{(p)}_{d}$-module, Noetherian      59
$\mathfrak{R}^{(\mathbb{K})}_{d}$      49
$\mathfrak{R}_{d}$      35
$\mathfrak{R}_{d}$-module      36
$\mathfrak{R}_{d}$-module, Noetherian      37
$\omega(n,F)$      231
$\Omega(X)_{-\infty}$      235
$\Omega(X)_{k}$      235
$\Omega(X,n)^{-}_{t}$      243
$\Omega(X,n)_{-\infty}$      243
$\Omega(X,n)_{t}$      243
$\overline{\mathbb{F}_{p}}$      43
$\overline{\mathbb{Q}}$      43
$\Sigma(\mathcal{A})$      108
$\widehat{\mathbb{Z}_{p}}$      30
Adele ring      62
adj(A)      91
Adjoint matrix      91 230
Algebraic number field      61
Algebraic unit      65
Almost block independent, sporadically      201
Almost block independent, universally      201
Almost box independent      201
Almost box independent, relatively      215
ann(a)      44
Annihilator      12 44
Arteen — Rees Lemma      49
Associated module      44
Associated prime ideal      44
Aut(X)      1
Automorphism      see "Group automorphism"
Bernoulli, factor      197
Bernoulli, measure      200
Bernoulli, shift      87
Borel sigma-algebra      2
C($\mu_{1}$,$\mu_{2}$)      199
C(X)      1
Cech homology      42
Cellular automaton      vii
centralizer      12
char($\mathfrak{R}_{d}/\mathfrak{p}$)      43
CHARACTER      2
Character, group      2
Characteristic      43
Characteristic, polynomial      37
Coboundary      293
Coboundary, algebraic      296
Cobounding function      293
Cocycle      293
Cocycle with summable variation      295
Cocycle, affine      295
Cocycle, algebraic      295
Cocycle, cohomologous      293
Cocycle, continuous      293
Cocycle, Hoelder      295
Cocycle, homomorphism      293
Cocycle, trivial      293
Completely positive entropy      162
Completion (w.r.t. a valuation)      61
Conditional entropy      108
Conditional expectation      xvi
Conditional information function      108
Conjugate, algebraically      2
Conjugate, measurably      2
Conjugate, to a full subshift      10
Conjugate, to a Lie subshift      10
Conjugate, to a subshift      10
Conjugate, topologically      2
Convolution      27 111 165
Coupling      199
Cyclotomic polynomial      see "Polynomial"
D.C.C.      see "Descending chain condition"
deg(f)      180
Descending chain condition      19
Dirichlet's L-function      ix
Dual $\mathbb{Z}^{d}$-action      35
Dual action      18
Dual automorphism      2
Dual group      2
Dual homomorphism      2
Dual module      36
Entropy of a $\mathbb{Z}^{d}$-action, metric      108
Entropy of a $\mathbb{Z}^{d}$-action, relative      242
Entropy of a $\mathbb{Z}^{d}$-action, topological      106
Entropy of a partition      108
Entropy, completely positive      162
Entropy, completely positive, on a sigma-algebra      162
Entropy, conditional      108
Entropy, dimension      226 227
Ergodic $\mathbb{Z}^{d}$-action      47
Ergodic group action by automorphisms      2
Ergodic group automorphism      2
Ergodic prime ideal      56
Ergodic probability measure      172
Ergodic subgroup      9
Expansive $\mathbb{Z}^{d}$-action      114
Expansive group action by automorphisms      2
Expansive group automorphism      2
Expansive neighbourhood      2
Expansive prime ideal      56
Expansive subgroup      9
Extension problem      32
F(n)      29
Face (of a convex set)      153 231
First cohomology group      293
Fourier transform      193
Frac(r)      67
Fractional part      67
Free module      90
Free orbit      122 123
gcd(a)      229
Generator (of a sigma-algebra for a group action)      109
Generators (of a module)      37
Group action by automorphisms      2
Group action by automorphisms, (strongly) mixing      2
Group action by automorphisms, ergodic      2
Group action by automorphisms, expansive      2
Group action by automorphisms, measure preserving      2
Group action by automorphisms, topologically transitive      2
Group action, transitive      165
Group automorphism      1
Group automorphism, dual      2
Group automorphism, ergodic      2
Group automorphism, expansive      2
Group automorphism, inner      1
Group automorphism, mixing      2
Group automorphism, topologically transitive      2
Group automorphism, trivial      1
Group of Markov type      24
Group of units      69
Group, character      2
Group, compact      1
Group, compact, Lie      1
Group, cyclic      23
Group, dual      2
Group, Polish      293
Group, polycyclic-by-finite      24
Group, ring      27
Group, torsion      44
Group, torsion-free      39 44
h($\alpha$)      109
Haar measure      2
Highest common factor of an ideal      229
Hoelder function      295
Hoelder structure      294
Homomorphism, central      11
Homomorphism, dual      2
Ideal, maximal      70
Ideal, principal      37
Indicator function      xvi
Inn(X)      1
Int(r)      67
Integral part      67
Invariant metric      1 3
Invariant probability measure      2 111
Invariant subgroup      1
J($\mu_{1}$,$\mu_{2}$)      199
Jensen's formula      126
joining      199
ker($\alpha$)      1
Kernel      1
Krull dimension      227
Laurent polynomial      35
Laurent polynomial, nice      206
Ledrappier's example      viii
Lehmer's problem      161
Lie subshift      10
Livshitz' theorem      294
Logarithmic height      137
Mahler measure      125
Markov subgroup      81
Markov type      24
Maximal compact subring      62
Measure of maximal entropy      195
Measure preserving, $\mathbb{Z}^{d}$-action      108
Measure preserving, group action by automorphisms      2
Measure preserving, isomorphism      2
Mixing, $\mathbb{Z}^{d}$-action      8
Mixing, group action by automorphisms      2
Mixing, group automorphism      2
Mixing, of all orders      262
Mixing, of order n      see "n-mixing"
Mixing, prime ideal      56
Mixing, probability measure      285
Mixing, subgroup      9
Module, associated      44
Module, cyclic      38
Module, free      90
Module, Noetherian      28 37
Module, torsion      44
Monomial      80
Morse sequence      291
1 2
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