Search results for "Markov partition"
showing 3 items of 3 documents
Variétés instables d'ensembles hyperboliques
1999
Resume Les varietes instables de systemes hyperboliques admettant une partition de Markov a un rectangle sont ici caracterisees a homeomorphisme pres et a conjugaison topologique (des dynamiques sous-jacentes) pres. De telles classes seront decrites a l'aide d'objets algebriques naturellement associes aux systemes sous-jacents.
Conjugate unstable manifolds and their underlying geometrized Markov partitions
2000
Abstract Conjugate unstable manifolds of saturated hyperbolic sets of Smale diffeomorphisms are characterized in terms of the combinatorics of their geometrized Markov partitions. As a consequence, the relationship between the local and the global point of view is also made explicit.
Counting Berg partitions via Sturmian words and substitution tilings
2013
We develop the connection of Berg partitions with special substitution tilings of two tiles. We obtain a new proof that the number of Berg partitions with a fixed connectivity matrix is equal to half of the sum of its entries, [12]. This approach together with the formula of Seebold [10], for the number of substitutions preserving a given Sturmian sequence, shows that all of the combinatorial substitutions can be realized geometrically as Berg partitions. We treat Sturmian tilings as intersection tilings of bi-partitions. Using the symmetries of bi-partitions we obtain geometrically the palindromic properties of Sturmian sequences (Theorem 3) established combinatorially by de Luca and Migno…