Description

• Title:
  Lifting ergodicity in $(G,\sigma)$-extension
• Creator:
  Nerurkar, Mahesh
• Description:
  Given a compact dynamical system $(X,T,m)$ and a pair $(G,\sigma)$ consisting of a compact group $G$ and a continuous group automorphism $\sigma$ of $G$, we consider the twisted skew-product transformation on $G\times X$ given by $$ T_\varphi (g,x) = (\sigma [(\varphi (x)g],Tx), $$ where $\varphi \colon X\rightarrow G$ is a continuous map. If $(X,T,m)$ is ergodic and aperiodic, we develop a new technique to show that for a large class of groups $G$, the set of $\varphi$'s for which the map $T_\varphi$ is ergodic (with respect to the product measure $\nu\times m$, where $\nu$ is the normalized Haar measure on $G$) is residual in the space of continuous maps from $X$ to $G$. The class of groups for which the result holds contains the class of all connected abelian and the class of all connected Lie groups. For the class of non-abelian fiber groups, this result is the only one of its kind.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2007.09.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 30, No 1 (September 2007); 193 - 210;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2007.025/8855
• Subject:
  Affine extensions;
  Dynamical Systems;
  ergodicity;
  cocycles;
  37A99;
  37A05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2007.025
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other