scholarly journals The entangled ergodic theorem in the almost periodic case

2010 ◽  
Vol 432 (2-3) ◽  
pp. 526-535 ◽  
Author(s):  
Francesco Fidaleo
Keyword(s):  
Ergodic Theorem ◽  
Periodic Case ◽  
Almost Periodic

scholarly journals ON THE ENTANGLED ERGODIC THEOREM

2007 ◽  
Vol 10 (01) ◽  
pp. 67-77 ◽  
Author(s):  
FRANCESCO FIDALEO
Keyword(s):  
Hilbert Space ◽  
Ergodic Theorem ◽  
Unitary Operator ◽  
Compact Operators ◽  
Ergodic Average ◽  
Periodic Case ◽  
Almost Periodic ◽  
Ergodic Averages ◽  
Weak Operator Topology ◽  
Weak Operator

Let U be a unitary operator acting on the Hilbert space [Formula: see text], and α: {1, …, m} ↦ {1, …, k} a partition of the set {1, …, m}. We show that the ergodic average [Formula: see text] converges in the weak operator topology if the Aj belong to the algebra of all the compact operators on [Formula: see text]. We write esplicitly the formula for these ergodic averages in the case of pair-partitions. Some results without any restriction on the operators Aj are also presented in the almost periodic case.

scholarly journals Noncommutative weighted individual ergodic theorems with continuous time

2020 ◽  
Vol 23 (02) ◽  
pp. 2050013
Author(s):  
Vladimir Chilin ◽  
Semyon Litvinov
Keyword(s):  
Ergodic Theorem ◽  
Continuous Time ◽  
Symmetric Spaces ◽  
Von Neumann Algebra ◽  
Ergodic Theorems ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Von Neumann ◽  
Marcinkiewicz Spaces ◽  
Local Ergodic Theorem

We show that ergodic flows in the noncommutative [Formula: see text]-space (associated with a semifinite von Neumann algebra) generated by continuous semigroups of positive Dunford–Schwartz operators and modulated by bounded Besicovitch almost periodic functions converge almost uniformly. The corresponding local ergodic theorem is also proved. We then extend these results to arbitrary noncommutative fully symmetric spaces and present applications to noncommutative Orlicz (in particular, noncommutative [Formula: see text]-spaces), Lorentz, and Marcinkiewicz spaces. The commutative counterparts of the results are derived.

scholarly journals Time Remotely Almost Periodic Viscosity Solutions of Hamilton-Jacobi Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Shilin Zhang ◽  
Daxiong Piao
Keyword(s):  
Viscosity Solutions ◽  
Existence And Uniqueness ◽  
Almost Periodic Functions ◽  
Periodic Case ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Jacobi Equations

We study some properties of the remotely almost periodic functions. This paper studies viscosity solutions of general Hamilton-Jacobi equations in the time remotely almost periodic case. Existence and uniqueness results are presented under usual hypotheses.

V.—Les transformations asymptotiquement presque périodiques discontinues et le lemme ergodique. (Première Note.)

1950 ◽  
Vol 63 (1) ◽  
pp. 61-68
Author(s):  
Maurice Fréchet
Keyword(s):  
Ergodic Theorem ◽  
Continuous Functions ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Discontinuous Functions ◽  
Extended Class ◽  
Class Of Functions ◽  
Asymptotically Almost Periodic

SynopsisWith the aim of establishing, under wide conditions, the ergodic theorem of G. D. Birkhoff, the author extends the class of asymptotically almost-periodic functions, considering now not only continuous functions, as he had already done in 1943, but discontinuous functions. Definitions and properties of the extended class of functions are set out, some comparisons being made with almost-periodic functions in the sense of Bohr, Stepanoff, Weyl and Besicovitch. Applications to the ergodic theorem are adumbrated.

Fractal dimensions of almost periodic attractors

1996 ◽  
Vol 16 (4) ◽  
pp. 791-803 ◽  
Author(s):  
Koichiro Naito
Keyword(s):  
Fractal Dimension ◽  
Periodic Orbits ◽  
Fractal Dimensions ◽  
Periodic Case ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Hölder Continuous ◽  
Periodic Attractors ◽  
Diophantine Approximations

AbstractIn this paper we estimate fractal dimensions of almost periodic orbits in terms of two kinds of exponents: the exponent in the inclusion lengths for ε-almost period and the exponent in Hölder conditions. Further, we estimate the inclusion lengths for ε-almost period of quasi-periodic functions by using Diophantine approximations. In the n-frequency quasi-periodic case we can show that the fractal dimension of its orbit is majorized by the value n/δ when it is Hölder continuous with exponent δ, 0 < δ ≤ 1.

scholarly journals Dynamics of a nonautonomous semiratio-dependent predator-prey system with nonmonotonic functional responses

2006 ◽  
Vol 2006 ◽  
pp. 1-19 ◽  
Author(s):  
Hai-Feng Huo ◽  
Wan-Tong Li
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Periodic Case ◽  
Almost Periodic ◽  
Functional Responses ◽  
Predator Prey ◽  
Prey System ◽  
Nonautonomous Case

A nonautonomous semiratio-dependent predator-prey system with nonmonotonic functional responses is investigated. For general nonautonomous case, positive invariance, permanence, and globally asymptotic stability for the system are studied. For the periodic (almost periodic) case, sufficient conditions for existence, uniqueness, and stability of a positive periodic (almost periodic) solution are obtained.

AN ERGODIC THEOREM FOR QUANTUM DIAGONAL MEASURES

2009 ◽  
Vol 12 (02) ◽  
pp. 307-320 ◽  
Author(s):  
FRANCESCO FIDALEO
Keyword(s):  
Ergodic Theorem ◽  
Classical Case ◽  
Product Measure ◽  
Natural Setting ◽  
Almost Periodic ◽  
Quantum Version

We prove the quantum version of an ergodic result of H. Furstenberg relative to noninvariant measures. The natural setting will be the case of the "quantum diagonal measure" relative to the product measure. Even if in all the interesting situations such diagonal measures are neither invariant nor normal with respect to the corresponding product ones, we still provide an ergodic theorem for them, generalizing the classical case. As a natural application, we are able to prove the entangled ergodic theorem in some interesting situations out of the known ones, that is when the unitary is not almost periodic, or when the involved operators are not compact.

PERMANENCE, AVERAGE PERSISTENCE AND EXTINCTION IN NONAUTONOMOUS SINGLE-SPECIES GROWTH CHEMOSTAT MODELS

2006 ◽  
Vol 09 (01n02) ◽  
pp. 41-58 ◽  
Author(s):  
MEHBUBA REHIM ◽  
ZHIDONG TENG
Keyword(s):  
Dilution Rate ◽  
Removal Rate ◽  
Single Species ◽  
Periodic Case ◽  
Response Functions ◽  
Almost Periodic ◽  
General Response ◽  
New Criteria

Non-autonomous single-species growth chemostat models with general response functions are considered. In the models, the dilution rate and removal rate are allowed to be different from each other. A series of new criteria on the boundedness, permanence, persistence, average persistence and extinction of the population is established. In particular, when models degenerate into the almost periodic case, the equivalences of the permanence, persistence and average persistence of species are obtained. These results improve and extend some well-known corresponding results obtained in Refs. 1, 14 and 17.

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