| Autor: |
Saeed Zakeri, Carsten Lunde Petersen |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
Advances in Mathematics. 361:106953 |
| ISSN: |
0001-8708 |
| DOI: |
10.1016/j.aim.2019.106953 |
| Popis: |
We study the combinatorial types of periodic orbits of the standard covering endomorphisms m k ( x ) = k x ( mod Z ) of the circle for integers k ≥ 2 and the frequency with which they occur. For any q-cycle σ in the permutation group S q , we give a full description of the set of period q orbits of m k that realize σ and in particular count how many such orbits there are. The description is based on an invariant called the “fixed point distribution” and is achieved by reducing the realization problem to finding the stationary state of an associated Markov chain. Our work generalizes earlier results on the special case where σ is a rotation cycle. It is motivated by the problem of understanding the combinatorial structure of the Julia sets of polynomial maps of degree ≥3 and their associated parameter spaces. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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