Year: 2021
Type: article
Abstract: We set up a real entropy function h R h_\Bbb {R} on the space M d ′ \mathcal {M}’_d of Möbius conjugacy classes of real rational maps of degree d d by assigning to each class the real entropy of a representative f ∈<!-- ∈ --> R ( z ) f\in \Bbb {R}(z) ; namely, the topological entropy of its restriction f ↾<!-- ↾ --> R ^<!-- ^ --> f\restriction _{\hat {\Bbb {R}}} to the real circle. We prove a rigidity result stating that h R h_\Bbb {R} is locally constant on the subspace determined by real maps quasi-conformally conjugate to f f . As examples of this result, we analyze real analytic stable families of hyperbolic and flexible Lattès maps with real coefficients along with numerous families of degree d d real maps of real entropy log <!-- --> ( d ) \log (d) . The latter discussion moreover entails a complete classification of maps of maximal real entropy.
DOI: 10.1090/ecgd/356
Author: Khashayar Filom
Institution: University of Michigan
Language: Latvian
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2793575785