Self similarity of the corrections to the ergodic theorem for the Pascal adic transformation
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English
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Self-similarity of the corrections to the ergodic theorem for the Pascal-adic transformation Elise Janvresse, Thierry de la Rue, Yvan Velenik Laboratoire de Mathematiques Raphael Salem CENTRE NATIONAL DE LA RECHERCHESCIENTIFIQUE T. de la Rue, E. Janvresse, Y. Velenik Self-similarity of the Pascal-adic transformation
- self-similar structure
- related problems
- transformation invariant measures
- adic transformation
- velenik self-similarity
Self-similarity of the corrections to
the ergodic theorem for the
Pascal-adic transformation
Elise Janvresse, Thierry de la Rue, Yvan Velenik
Laboratoire de Mathematiques Raphael Salem
CENTRE NATIONAL
DE LA RECHERCHE
SCIENTIFIQUE
T. de la Rue, E. Janvresse, Y. Velenik Self-similarity of the Pascal-adic transformationThe Pascal-adic transformation
Introduction to the transformation
Self-similar structure of the basic blocks
Invariant measures
Ergodic interpretation
Coding: basic blocks
Generalizations and related problems
1 The Pascal-adic transformation
2 Self-similar structure of the basic blocks
3 Ergodic interpretation
4 Generalizations and related problems
T. de la Rue, E. Janvresse, Y. Velenik Self-similarity of the Pascal-adic transformationThe Pascal-adic transformation
Introduction to the transformation
Self-similar structure of the basic blocks
Invariant measures
Ergodic interpretation
Coding: basic blocks
Generalizations and related problems
Pascal Graph
T. de la Rue, E. Janvresse, Y. Velenik Self-similarity of the Pascal-adic transformationSelf-similarity of the Pascal-adic transformation
Pascal Graph
The Pascal-adic transformation
Introduction to the transformation
Pascal Graph
The Pascal graph: it is composed of in nitely many vertices
and edges.
2005-03-31The Pascal-adic transformation
Introduction to the transformation
Self-similar structure of the basic blocks
Invariant measures
Ergodic interpretation
Coding: basic blocks
Generalizations and related problems
Pascal Graph
1
2
n
T. de la Rue, E. Janvresse, Y. Velenik Self-similarity of the Pascal-adic transformationThe Pascal-adic transformation
Introduction to the transformation
Self-similar structure of the basic blocks
Invariant measures
Ergodic interpretation
Coding: basic blocks
Generalizations and related problems
Pascal Graph
1
2
n
(n,0) (n,k) (n,n)
T. de la Rue, E. Janvresse, Y. Velenik Self-similarity of the Pascal-adic transformationSelf-similarity of the Pascal-adic transformation
Pascal Graph
The Pascal-adic transformation
1
2
Introduction to the transformation
n
(n,0) (n,k) (n,n)Pascal Graph
Its vertices are arranged in levels numbered 0,1,2,...,n,...
Level n contains (n+1) vertices, denoted by
(n,0),(n,1),...,(n,k),...,(n,n). Each vertex (n,k) is
connected to two vertices at level n+1: (n+1,k) and
(n+1,k +1).
2005-03-31The Pascal-adic transformation
Introduction to the transformation
Self-similar structure of the basic blocks
Invariant measures
Ergodic interpretation
Coding: basic blocks
Generalizations and related problems
Pascal Graph
1
2
n
(n,0) (n,k) (n,n)
T. de la Rue, E. Janvresse, Y. Velenik Self-similarity of the Pascal-adic transformationSelf-similarity of the Pascal-adic transformation
Pascal Graph
The Pascal-adic transformation
1
2
Introduction to the transformation
n
(n,0) (n,k) (n,n)Pascal Graph
We are interested in trajectories on this graph, starting from
the 0-level vertex (the root) and going successively through all
its levels.
2005-03-31The Pascal-adic transformation
Introduction to the transformation
Self-similar structure of the basic blocks
Invariant measures
Ergodic interpretation
Coding: basic blocks
Generalizations and related problems
Pascal Graph
0 1x=01100100111...
1
2
n
(n,0) (n,k) (n,n)
T. de la Rue, E. Janvresse, Y. Velenik Self-similarity of the Pascal-adic transformation
