Stronger forms of sensitivity for dynamical systems

  title={Stronger forms of sensitivity for dynamical systems},
  author={T. K. Subrahmonian Moothathu tksm}
  • T. K. Subrahmonian Moothathu tksm
For continuous self-maps of compact metric spaces, we initiate a preliminary study of stronger forms of sensitivity formulated in terms of ‘large’ subsets of N. Mainly we consider ‘syndetic sensitivity’ and ‘cofinite sensitivity’. We establish the following: (i) any syndetically transitive, non-minimal map is syndetically sensitive (this improves the result that sensitivity is redundant in Devaney’s definition of chaos), (ii) any sensitive map of [0, 1] is cofinitely sensitive, (iii) any… CONTINUE READING