''of a dynamical system''
[[Category:Ergodic theory]]
1 KB (242 words) - 21:18, 8 November 2014
$#C+1 = 14 : ~/encyclopedia/old_files/data/H047/H.0407820 Homology of a dynamical system,
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4 KB (528 words) - 22:10, 5 June 2020
A [[flow (continuous-time dynamical system)]] the trajectories of which become almost-periodic after a certain
In the above, an almost-periodic trajectory in a [[dynamical system]] $\{ S^t \}$ on a metric space $(X,\rho)$ is the trajectory of any
1,020 bytes (154 words) - 19:16, 25 October 2014
$#C+1 = 7 : ~/encyclopedia/old_files/data/M062/M.0602950 Maximal ergodic theorem
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2 KB (340 words) - 08:12, 9 January 2024
...our of the system resembles that of a [[Gradient dynamical system|gradient dynamical system]] (see [[#References|[1]]], [[#References|[2]]]).
...valign="top"> A.N. Sharkovskii, V.A. Dobrynskii, , ''Dynamical systems and problems of stability of solutions of differential equations'' , Kiev (197
3 KB (395 words) - 10:06, 24 August 2014
''$\{T_t\}$ with phase space $X$ and invariant measure $\mu$
A common name for various spectral invariants and spectral properties of the corresponding group (or semi-group) of unitary (
5 KB (710 words) - 12:58, 16 July 2014
[[Category:Ergodic theorems, spectral theory, Markov operators]]
...$ T $ of a $ \sigma $-finite measure space $ (X,\Sigma,\mu) $, Birkhoff’s ergodic theorem states that for any function $ f \in {L^{1}}(X,\Sigma,\mu) $, the l
3 KB (460 words) - 05:51, 29 November 2016
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...re|measure]] when $X$ is a shift space (cf. [[Shift dynamical system|Shift dynamical system]]). The importance of absolutely continuous invariant measures is du
5 KB (722 words) - 16:46, 1 July 2020
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[[Category:Measure-theoretic ergodic theory]]
2 KB (260 words) - 08:00, 6 June 2020
$#C+1 = 22 : ~/encyclopedia/old_files/data/O068/O.0608360 Operator ergodic theorem
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5 KB (685 words) - 16:32, 6 January 2024
$#C+1 = 36 : ~/encyclopedia/old_files/data/V096/V.0906910 von Neumann ergodic theorem
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4 KB (632 words) - 17:38, 6 January 2024
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[[Category:Ergodic theory]]
5 KB (696 words) - 08:01, 6 June 2020
$#C+1 = 34 : ~/encyclopedia/old_files/data/S084/S.0804890 Shift dynamical system
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6 KB (862 words) - 08:13, 6 June 2020
...31 : ~/encyclopedia/old_files/data/F040/F.0400650 Flow (continuous\AAhtime dynamical system)
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3 KB (541 words) - 19:39, 5 June 2020
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...nd [[Topological dynamics|topological dynamics]] used in phrases like: "a dynamical system (flow, cascade or transformation generating the latter) has a quasi-
7 KB (978 words) - 05:56, 19 March 2022
...t\}$ (of a [[Flow (continuous-time dynamical system)|flow (continuous-time dynamical system)]] or of a [[Cascade|cascade]]) with phase space $X$''
...trarily large countable transfinite number even for flows in $\mathbf R^3$ and on certain open surfaces (see [[#References|[8]]]–[[#References|[10]]]).
4 KB (617 words) - 16:07, 19 August 2014
$#C+1 = 71 : ~/encyclopedia/old_files/data/E035/E.0305760 Entropy theory of a dynamical system
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7 KB (1,040 words) - 19:23, 13 January 2024
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is the partition into points; and c) the only measurable partition $ \mathop{\rm mod} 0 $
7 KB (1,037 words) - 16:58, 1 July 2020
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...eir generalization — a sequence of independent trials with the same result and with the same probability distribution.
4 KB (566 words) - 10:58, 29 May 2020
...somorphic, and therefore one often does not distinguish between the states and the phase points that represent them.
...ary to consider statistical states of systems; for classical (non-quantum) systems they are described by probability distributions on the phase space. The rul
6 KB (906 words) - 21:49, 30 April 2014