Stochastic Stability in Some Chaotic Dynamical Systems.
Strict measure rigidity for unipotent subgroups of solvable groups.
Strict Uniformity in Ergodic Theory.
Stricte ergodicité des échanges d'intervalles.
Strictly ergodic Toeplitz flows with positive entropies and trivial centralizers
A class of strictly ergodic Toeplitz flows with positive entropies and trivial topological centralizers is presented.
Strictly ergodic, uniform positive entropy models
Strong estimate for square functions in higher dimensions.
Strongly Mixing g-Measures.
Strongly mixing sequences of measure preserving transformations
We call a sequence of measure preserving transformations strongly mixing if tends to for arbitrary measurable , . We investigate whether one can pass to a suitable subsequence such that almost surely for all (or “many”) integrable .
Structure of mixing and category of complete mixing for stochastic operators
Let T be a stochastic operator on a σ-finite standard measure space with an equivalent σ-finite infinite subinvariant measure λ. Then T possesses a natural "conservative deterministic factor" Φ which is the Frobenius-Perron operator of an invertible measure preserving transformation φ. Moreover, T is mixing ("sweeping") iff φ is a mixing transformation. Some stronger versions of mixing are also discussed. In particular, a notion of *L¹-s.o.t. mixing is introduced and characterized in terms of weak...
Structure of the group of homeomorphisms preserving a good measure on a compact manifold
Subadditive maximal ergodic theorem
Sublinear functionals ergodicity and finite invariant measures.
Subshifts of Finite Type and Sofic Systems.
Suites de -orbite finie.
Suites équiréparties et ensembles mesurables au sens de Riemann
S-unimodal Misiurewicz maps with flat critical points
We consider S-unimodal Misiurewicz maps T with a flat critical point c and show that they exhibit ergodic properties analogous to those of interval maps with indifferent fixed (or periodic) points. Specifically, there is a conservative ergodic absolutely continuous σ-finite invariant measure μ, exact up to finite rotations, and in the infinite measure case the system is pointwise dual ergodic with many uniform and Darling-Kac sets. Determining the order of return distributions to suitable reference...
Support as an invariant for dynamical systems
Support overlapping contractions and exact non-singular transformations
Let T be a positive linear contraction of of a σ-finite measure space (X,Σ,μ) which overlaps supports. In general, T need not be completely mixing, but it is in the following cases: (i) T is the Frobenius-Perron operator of a non-singular transformation ϕ (in which case complete mixing is equivalent to exactness of ϕ). (ii) T is a Harris recurrent operator. (iii) T is a convolution operator on a compact group. (iv) T is a convolution operator on a LCA group.
Sur certains éléments ergodiques dans