For a certain parametrized family of maps on a circle with critical points and logarithmic singularities where derivatives blow up to infinity, we construct a positive measure set of parameters corresponding to maps which exhibit nonuniformly expanding behaviour. This implies the existence of "chaotic" dynamics in dissipative homoclinic tangles in periodically perturbed differential equations.
|Number of pages||18|
|Publication status||Published - 2012 Feb|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics