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Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere

Ľubomír Baňas, Zdzisław Brzeźniak, Mikhail Neklyudov, Martin Ondreját, Andreas Prohl (2015)

Czechoslovak Mathematical Journal

We study ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere while considering only solutions which are independent of the space variable. This simplification leads to a degenerate stochastic equation in the tangent bundle of the 2D sphere. Studying this equation, we prove existence and non-uniqueness of invariant probability measures for the original problem and obtain also results on attractivity towards an invariant measure. We also...

Ergodicity of ℤ² extensions of irrational rotations

Yuqing Zhang (2011)

Studia Mathematica

Let = [0,1) be the additive group of real numbers modulo 1, α ∈ be an irrational number and t ∈ . We study ergodicity of skew product extensions T : × ℤ² → × ℤ², T ( x , s , s ) = ( x + α , s + 2 χ [ 0 , 1 / 2 ) ( x ) - 1 , s + 2 χ [ 0 , 1 / 2 ) ( x + t ) - 1 ) .

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