Displaying similar documents to “Structure of mixing and category of complete mixing for stochastic operators”

On a one-dimensional analogue of the Smale horseshoe

Ryszard Rudnicki (1991)

Annales Polonici Mathematici

Similarity:

We construct a transformation T:[0,1] → [0,1] having the following properties: 1) (T,|·|) is completely mixing, where |·| is Lebesgue measure, 2) for every f∈ L¹ with ∫fdx = 1 and φ ∈ C[0,1] we have ∫ φ ( T n x ) f ( x ) d x → ∫ φ d μ , where μ is the cylinder measure on the standard Cantor set, 3) if φ ∈ C[0,1] then n - 1 ∑ i = 0 n - 1 φ ( T i x ) → ∫ φ d μ for Lebesgue-a.e. x.

Analytic nonregular cocycles over irrational rotations

Mariusz Lemańczyk (1995)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Analytic cocycles of type I I I 0 over an irrational rotation are constructed and an example of that type is given, where all corresponding special flows are weakly mixing.

On recent progress for the stochastic Navier Stokes equations

Jonathan Mattingly (2003)

Journées équations aux dérivées partielles

Similarity:

We give an overview of the ideas central to some recent developments in the ergodic theory of the stochastically forced Navier Stokes equations and other dissipative stochastic partial differential equations. Since our desire is to make the core ideas clear, we will mostly work with a specific example : the stochastically forced Navier Stokes equations. To further clarify ideas, we will also examine in detail a toy problem. A few general theorems are given. Spatial regularity, ergodicity,...

Continuous subadditive processes and formulae for Lyapunov characteristic exponents

Wojciech Słomczyński (1995)

Annales Polonici Mathematici

Similarity:

Asymptotic properties of various semidynamical systems can be examined by means of continuous subadditive processes. To investigate such processes we consider different types of exponents: characteristic, central, singular and global exponents and we study their properties. We derive formulae for central and singular exponents and show that they provide upper bounds for characteristic exponents. The concept of conjugate processes introduced in this paper allows us to find lower bounds...