From zero to positive entropy

Enrique Pujals (CUNY)

We will discuss the mathematical processes by which a system evolves from one whose recurrent set is finite towards another one exhibiting chaotic behavior as parameters governing the behavior of the system are varied. In that direction, we will present a tentative global framework toward describing a large class of two-dimensional dynamics (that includes the Henon family), inspired partially by the developments in the one-dimensional theory of interval maps. More precisely, we present a class of intermediate smooth dynamics between one and higher dimensions where it is possible to describe the transition from zero to positive entropy.