Infinite-modal maps with global chaotic behavior


We prove that certain parametrized families of one-dimensional maps with infinitely many critical points exhibit global chaotic behavior in a persistent way: For a positive Lebesgue measure set of parameter values the map is transitive and almost every orbit has positive Lyapunov exponent. An application of these methods yields a proof of existence and even persistence of global spiral attractors for smooth flows in three dimensions, to be given in [5].


María José Pacifico

Álvaro Rovella

Marcelo Viana