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An important approach to establishing stochastic behavior of dynamical systems is based on the study of systems expanding a foliation and of measures having smooth densities along
the leaves of this ...
REGULARITY OF ABSOLUTELY CONTINUOUS INVARIANT MEASURES FOR PIECEWISE EXPANDING UNIMODAL MAPS
INVARIANT MEASURES UNIMODAL MAPS
2015/9/29
An important discovery of the 20th century mathematics is that many deterministic
systems exhibit stochastic behavior. The stochasticity is caused by exponential divergence of nearby trajectories. Th...
Martin-Lof randomness, invariant measures and countable homogeneous structurs
Martin-Lof randomness topological dynamics amenable groups Fraisse limits Ramsey theory
2012/5/24
We use ideas from topological dynamics (amenability), combinatorics (structural Ramsey theory) and model theory (Fra\" {i}ss\' e limits) to study closed amenable subgroups $G$ of the symmetric group $...
Invariant Measures with Bounded Variation Densities for Piecewise Area Preserving Maps
Bounded Variation Piecewise Area Preserving Maps Dynamical Systems
2011/8/30
Abstract: We investigate the properties of absolutely continuous invariant probability measures (ACIPs) for piecewise area preserving maps (PAPs) on $\mathbb{R}^d$. This class of maps unifies piecewis...
On the finite-dimensional marginals of shift-invariant measures
On the finite-dimensional marginals shift-invariant measures
2010/11/17
Let $\Sigma$ be a finite alphabet, $\Omega=\Sigma^{\mathbb{Z}^{d}}$ equipped with the shift action, and $\mathcal{I}$ the simplex of shift-invariant measures on $\Omega$. We study the relation betwee...