2017/08/11 by Yong Moo Chung, Hiroki Takahasi, Chung, Yong Moo +1
Mathematics · Physics and Astronomy · #37C40 #37C45 #37D25 #37D35 #37E05 #60F10 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Quantum chaos and dynamical systems #Theoretical and Computational Physics #math.DS #math.PR #msc:37C40 #msc:37C45 #msc:37D25 #msc:37D35 #msc:37E05 #msc:60F10
paper · pdf · doi:10.48550/arxiv.1708.03695
35 pages, 1 figure
openalex publication_date 2017/08/11 · arxiv created 2017/12/18 · arxiv updated 2017/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.