Chaos of Transformations Induced Onto the Space of Probability Measures

@article{Wu2016ChaosOT,
  title={Chaos of Transformations Induced Onto the Space of Probability Measures},
  author={Xinxing Wu},
  journal={I. J. Bifurcation and Chaos},
  year={2016},
  volume={26},
  pages={1-12}
}
For a dynamical system (X, T ), let (M(X), TM ) be its induced dynamical system on the space of Borel probability measures with weak*-topology. It is proved that (M(X), TM ) is a-transitive (resp., exact, uniformly rigid) if and only if (X, T ) is weakly mixing and a-transitive (resp., exact, uniformly rigid), where a is an n-vector of integers. Moreover… CONTINUE READING