منابع مشابه
Symbolic Dynamics and Markov Partitions
The decimal expansion of real numbers, familiar to us all, has a dramatic generalization to representation of dynamical system orbits by symbolic sequences. The natural way to associate a symbolic sequence with an orbit is to track its history through a partition. But in order to get a useful symbolism, one needs to construct a partition with special properties. In this work we develop a genera...
متن کاملJ ul 1 99 6 SYMBOLIC DYNAMICS AND MARKOV PARTITIONS
The decimal expansion real numbers, familiar to us all, has a dramatic generalization to representation of dynamical system orbits by symbolic sequences. The natural way to associate a symbolic sequence with an orbit is to track its history through a partition. But in order to get a useful symbolism, one needs to construct a partition with special properties. In this work we develop a general t...
متن کاملSymbolic Dynamics and Markov Partitions for the Stadium Billiard
We investigate the Bunimovich stadium dynamics and nd that in the limit of innnitely long stadium the symbolic dynamics is a subshift of nite type. For a stadium of nite length the Markov partitions are innnite, but the inadmissible symbol sequences can be determined exactly by means of the appropriate pruning front. We outline a construction of a sequence of nite Markov graph approximations by...
متن کاملMarkov Partitions and Homoclinic Pointsof
We prove that a general class of expansive Z d-actions by automorphisms of compact, abelian groups with completely positive en-tropy has`symbolic covers' of equal topological entropy. These symbolic covers are constructed by using homoclinic points of these actions. For d = 1 we adapt a result of Kenyon and Vershik in 7] to prove that these symbolic covers are, in fact, sooc shifts. For d 2 we ...
متن کاملA Approximate Verification of the Symbolic Dynamics of Markov Chains
A finite state Markov chain M can be regarded as a linear transform operating on the set of probability distributions over its node set. The iterative applications of M to an initial probability distribution μ0 will generate a trajectory of probability distributions. Thus a set of initial distributions will induce a set of trajectories. It is an interesting and useful task to analyze the dynami...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1998
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-98-00737-x