Ergodicity of Skew Product Action

• 발행기관: 호서대학교 기초과학연구소
• 저자명: 김현정
• 간행물 정보: 『기초과학연구 논문집』제26권 제1호, 105~111쪽, 전체 7쪽
• 주제분류: 공학 > 공학일반
• 파일형태: PDF
• 발행일자: 2018.12.30

영문 초록

Let (X, Ω, μ)be a nonatomic standard Borel space with probability measure μ. Let G be a locally compact second countable group with Haar measure λ. and with Borel field B. Let Γ be a countable automorphism group preserving the measure μ and acting ergodically in X by a Borel action. In Kim, it has been proved that supposing Γ is acting on (X, Ω, μ) ergodically, the skew product action (X ×a G, Γ) is ergodic if and only if the cocycle α has a dense range in G. Using this theorem, we have that the following theorem : Suppose that Γ is a Fuchsian group acting on a 2 - dimensioanl Riemannian manifold H of the constant sectional curvature - 1 and Hor(H) the space of horospheres in H. Then we have The Γ - action on the ideal boundary ∂H of H is ergodic and Γ-action on Hor(H) = ∂H × β R is also ergodic for some cocycle β : Γ × H → R.

목차

Abstract

Ⅰ. 서론

Ⅱ. 본론

Ⅳ. 참고문헌

키워드

cocycle skew product action horocycle ergodic