## Infinite-modal maps with global chaotic behavior.(English)Zbl 0916.58029

Ann. Math. (2) 148, No. 2, 441-484 (1998); Corrigendum 149, No. 2, 705 (1999).
The main goal is to study the dynamics of certain parametrized families $$(f_\mu)_\mu$$ of one-dimensional maps with infinite critical set. The authors show that they exhibit global chaotic behaviour 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. This class of systems is motivated by a problem in the dynamics of flows in three dimensions: the unfolding of saddle-focus homoclinic connections.

### MSC:

 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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