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Search: MSC category 37B10 ( Symbolic dynamics [See also 37Cxx, 37Dxx] )

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1. CJM 2011 (vol 64 pp. 1341)

Killough, D. B.; Putnam, I. F.
 Bowen Measure From Heteroclinic Points We present a new construction of the entropy-maximizing, invariant probability measure on a Smale space (the Bowen measure). Our construction is based on points that are unstably equivalent to one given point, and stably equivalent to another: heteroclinic points. The spirit of the construction is similar to Bowen's construction from periodic points, though the techniques are very different. We also prove results about the growth rate of certain sets of heteroclinic points, and about the stable and unstable components of the Bowen measure. The approach we take is to prove results through direct computation for the case of a Shift of Finite type, and then use resolving factor maps to extend the results to more general Smale spaces. Keywords:hyperbolic dynamics, Smale spaceCategories:37D20, 37B10

2. CJM 2001 (vol 53 pp. 382)

Pivato, Marcus
 Building a Stationary Stochastic Process From a Finite-Dimensional Marginal If $\mathfrak{A}$ is a finite alphabet, $\sU \subset\mathbb{Z}^D$, and $\mu_\sU$ is a probability measure on $\mathfrak{A}^\sU$ that looks like'' the marginal projection of a stationary stochastic process on $\mathfrak{A}^{\mathbb{Z}^D}$, then can we extend'' $\mu_\sU$ to such a process? Under what conditions can we make this extension ergodic, (quasi)periodic, or (weakly) mixing? After surveying classical work on this problem when $D=1$, we provide some sufficient conditions and some necessary conditions for $\mu_\sU$ to be extendible for $D>1$, and show that, in general, the problem is not formally decidable. Categories:37A50, 60G10, 37B10