Invariant measures of selfsimilar sets. (Mesures invariantes sur des ensembles autosimilaires.) (French) Zbl 1120.37302

Guillopé, Laurent

Seminar on spectral theory and geometry, 1987-1988. Chambéry: Univ. de Savoie, Fac. des Sciences, Service de Math.; St. Martin d’Hères: Univ. de Grenoble I, Inst. Fourier. Sémin. Théor. Spectrale Géom., Chambéry-Grenoble 6, 49-60 (1988).

Summary: With every finite family \(S\) of contraction mappings we associate a self-similar limit set. There exists an invariant measure for certain Markov processes constructed from the family \(S\), and some recent theorems for approximating this measure à la Birkhoff are at the basis of the techniques of image compression.
For the entire collection see [Zbl 0825.00041].

MSC:

37A05	Dynamical aspects of measure-preserving transformations
60J05	Discrete-time Markov processes on general state spaces
28D05	Measure-preserving transformations
68U10	Computing methodologies for image processing

Keywords:

selfsimilar limit set; invariant measure; Markov processes; image compression; Birkhoff measure