A pr 2 00 8 CENTRAL LIMIT THEOREMS FOR NON - INVERTIBLE MEASURE PRESERVING MAPS
نویسندگان
چکیده
Using the Perron-Frobenius operator we establish a new functional central limit theorem result for non-invertible measure preserving maps that are not necessarily ergodic. We apply the result to asymptotically periodic transformations and give an extensive specific example using the tent map.
منابع مشابه
Central Limit Theorems for Non-invertible Measure Preserving Maps
This paper is motivated by the question “How can we produce the characteristics of a Wiener process (Brownian motion) from a semi-dynamical system?”. This question is intimately connected with Central Limit Theorems for non-invertible maps and various invariance principles. Many results on CLT and invariance principles for maps have been proved, see e.g. the surveys Denker [4] and Mackey and Ty...
متن کاملA pr 2 00 7 ERGODIC THEORY : RECURRENCE
Almost every, essentially: Given a Lebesgue measure space (X,B, μ), a property P (x) predicated of elements of X is said to hold for almost every x ∈ X, if the set X \ {x : P (x) holds} has zero measure. Two sets A,B ∈ B are essentially disjoint if μ(A ∩B) = 0. Conservative system: Is an infinite measure preserving system such that for no set A ∈ B with positive measure are A,T−1A,T−2A, . . . p...
متن کاملNew operators through measure of non-compactness
In this article, we use two concepts, measure of non-compactness and Meir-Keeler condensing operators. The measure of non-compactness has been applied for existence of solution nonlinear integral equations, ordinary differential equations and system of differential equations in the case of finite and infinite dimensions by some authors. Also Meir-Keeler condensing operators are shown in some pa...
متن کاملar X iv : m at h / 03 11 20 9 v 1 [ m at h . D S ] 1 3 N ov 2 00 3 DISSIPATION TIME AND DECAY OF CORRELATIONS
We consider the effect of noise on the dynamics generated by volume-preserving maps on a d-dimensional torus. The quantity we use to measure the irreversibility of the dynamics is the dissipation time. We focus on the asymptotic behaviour of this time in the limit of small noise. We derive universal lower and upper bounds for the dissipation time in terms of various properties of the map and it...
متن کاملN ov 2 00 3 DISSIPATION TIME AND DECAY OF CORRELATIONS
We consider the effect of noise on the dynamics generated by volume-preserving maps on a d-dimensional torus. The quantity we use to measure the irreversibility of the dynamics is the dissipation time. We focus on the asymptotic behaviour of this time in the limit of small noise. We derive universal lower and upper bounds for the dissipation time in terms of various properties of the map and it...
متن کامل