Invariant measures for iterated function systems
نویسندگان
چکیده
منابع مشابه
Iterated function systems, Ruelle operators, and invariant projective measures
We introduce a Fourier-based harmonic analysis for a class of discrete dynamical systems which arise from Iterated Function Systems. Our starting point is the following pair of special features of these systems. (1) We assume that a measurable space X comes with a finite-to-one endomorphism r : X → X which is onto but not one-to-one. (2) In the case of affine Iterated Function Systems (IFSs) in...
متن کاملRigorous Approximation of Stationary Measures for Iterated Function Systems
We study the problem of the rigorous computation of the stationary measure of an IFS described by a stochastic mixture of two or more dynamical systems which are either all uniformly expanding on the interval, either all contractive. In the expanding case, the associated transfer operators satisfy a LasotaYorke inequality, and we compute rigorously the approximations in the L1 norm. The rigorou...
متن کاملA Note on Invariant Sets of Iterated Function Systems
We prove that the family of all invariant sets of iterated systems of contractions R → R is a nowhere dense Fσ type subset in the space of the non-empty compact subsets of R equipped with the Hausdorff metric. An iterated function system (IFS for short) is a finite collection (T1, . . . , Tn) of weak contractions of a metric space X. By a weak contraction we mean a mapping T : X → X such that d...
متن کاملA family of measures associated with iterated function systems
Let (X, d) be a compact metric space, and let an iterated function system (IFS) be given on X, i.e., a finite set of continuous maps σi: X → X, i = 0, 1, · · · , N − 1. The maps σi transform the measures μ on X into new measures μ i . If the diameter of σi1 ◦ · · · ◦ σik (X) tends to zero as k → ∞, and if pi > 0 satisfies ∑ i pi = 1, then it is known that there is a unique Borel probability mea...
متن کاملIterated Function Systems with Overlaps and Self-similar Measures
The paper considers the iterated function systems of similitudes which satisfy a separation condition weaker than the open set condition, in that it allows overlaps in the iteration. Such systems include the well-known Bernoulli convolutions associated with the PV numbers, and the contractive similitudes associated with integral matrices. The latter appears frequently in wavelet analysis and th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 2000
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap-75-1-87-98