On ergodicity of some cylinder flows

• Autorzy: Krzysztof M. Frączek
• Języki publikacji: EN

Abstrakty

EN

We study ergodicity of cylinder flows of the form
  $T_f:{\sym T}×ℝ → {\sym T}×ℝ$, $T_f(x,y) = (x+α,y+f(x))$,
where $f:{\sym T} → ℝ$ is a measurable cocycle with zero integral. We show a new class of smooth ergodic cocycles. Let k be a natural number and let f be a function such that $D^kf$ is piecewise absolutely continuous (but not continuous) with zero sum of jumps. We show that if the points of discontinuity of $D^kf$ have some good properties, then $T_f$ is ergodic. Moreover, there exists $ε_f > 0$ such that if $v:{\sym T}→ℝ$ is a function with zero integral such that $D^kv$ is of bounded variation with $Var(D^kv) < ε_f$, then $T_{f+v}$ is ergodic.

Kategorie tematyczne

• 37C40: Smooth ergodic theory, invariant measures
• 37A05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2000
• Tom: 163
• Numer: 2
• Strony: 117-130

Daty

wydano

2000

otrzymano

1998-11-16

Twórcy

autor

Krzysztof M. Frączek

• Faculty of Mathematics and Computer, Science Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

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