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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
n-mixing      169
Noether's normalization lemma      71
Non-mixing set      see "Set non-mixing"
o(c)      64
octahedron      157
Ostrowski's theorem      61
Out(X)      1
p($\mathfrak{p}$)      43
p-adic integers      18
p-adic rationals      61
Per($\alpha$)      94
Period      40
Periodic point      39
Pinsker algebra      162
Place      61
Place above a place v      61
Place below a place v      61
Place, complex      62
Place, finite      61
Place, infinite      61
Place, real      62
Polynomial in a single variable, generalized      271
Polynomial, cyclotomic      47
Polynomial, cyclotomic, generalized      47
Polynomial, Laurent      35
Polynomial, Laurent, nice      206
Polynomial, trigonometric      204
Pontryagin's duality theorem      2
Primary submodule      44
Prime element      62
Prime field      43
Prime filtration      45
Prime ideal, associated      44
Prime ideal, ergodic      56
Prime ideal, expansive      56
Prime ideal, mixing      56
Prime ideal, null      152
Prime ideal, positive      152
Primitive element of $\mathbb{Z}^{d}$      70
Primitive Laurent polynomial      39
Primitive subgroup of $\mathbb{Z}^{d}$      70
Primitive unit root      180
Principal ideal domain      56
Product, action      24
Product, formula      136
Quotient action      77
r($\mathfrak{p}$)      71 73
Radical ideal      69
Reduced primary decomposition      44
Relative entropy      242
Residual sigma-algebra      242
Right Noetherian ring      27
S-unit      267
Self-conjugacy      297
Separated set      see "Set separated"
Set of associated primes      44
Set, $\lambda_{X}$-non-mixing      287
Set, $\mu$-non-mixing      287
Set, (Q,$\delta$,$\varepsilon$)-separated      105
Set, (Q,$\delta$,$\varepsilon$)-spanning      105
Set, follower      25 83
Set, incontractible      276
Set, mixing      261
Set, non-mixing      261
Set, non-mixing, extremal      275
Set, non-mixing, minimal      276
Set, predecessor      83
Set, [Q,$\delta$,$\varepsilon$]-separated      112
Set, [Q,$\delta$,$\varepsilon$]-spanning      112
Shift of finite type      22
Shift-action of $\mathbb{Z}^{d}$      36
Shift-action of a countable group      9
Shift-invariant, probability measure      198
Shift-invariant, probability measure, almost box independent      201
Shift-invariant, probability measure, Bernoulli      200
Shift-invariant, probability measure, sporadically a.b.i.      201
Shift-invariant, probability measure, summably Vershik      201
Shift-invariant, probability measure, universally a.b.i.      201
Shift-invariant, subgroup      9
Shift-invariant, subgroup of finite type      22
Shift-invariant, subgroup, ergodic      9
Shift-invariant, subgroup, expansive      9
Shift-invariant, subgroup, mixing      9
Shift-periodic      95
Solenoid      57
Spanning set      see "Set spanning"
Standard measure space      xvi
State partition      222
SU(N)      xvi
Subgroup of finite type      22
Subgroup, full      9
Subgroup, invariant      1
Subgroup, Markov      81
Subgroup, shift-invariant      9
Subgroup, shift-invariant, ergodic      9
Subgroup, shift-invariant, expansive      9
Subgroup, shift-invariant, mixing      9
Subgroup, stability      123
Submodule      28 37
Submodule, primary      44
Subshift of finite type      vii 22 32
Summable variation      294
Summably Vershik      201
Support      27 144 270
Supporting hyperplane      153
Tiling      201
Topologically transitive, group action by automorphisms      2
Topologically transitive, group automorphism      2
Torsion, group      44
Torsion, module      44
Torsion-free group      39
Transfer function      293
Transpose matrix      7
Ultrametric inequality      135
Uniform topology      1
V($\mathfrak{p}$)      44
v-adic topology      61
Valuation      61
Valuation, archimedean      61
Valuation, equivalent      61
Valuation, non-archimedean      61
Valuation, non-trivial      61
Variational Principle      111
Variety      44
Width (of a convex set)      231
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