Large Deviation Principle for $S$-unimodal maps with flat critical point

Abstract

We study a topologically exact, negative Schwarzian unimodal map whose critical point is non-recurrent and flat. Assuming the critical order is either logarithmic or polynomial, we establish the Large Deviation Principle and give a partial description of the zeros of the corresponding rate functions. We apply our main results to a certain parametrized family of unimodal maps in the same topological conjugacy class, and give a complete description of the zeros of the rate functions. We observe a qualitative change at a transition parameter, and show that the sets of zeros depend continuously on the parameter even at the transition.

35 pages, 1 figure

References in corpus (1)

• Statistical stability of equilibrium states for interval maps

Cited by in corpus (1)

• Large deviation principle for harmonic/geometric/arithmetic mean of digits in backward continued fraction expansion