A class of adding machines and Julia sets
| Autor: | Danilo Antonio Caprio |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Adding machine
Sequence Fibonacci number Endomorphism Markov chain Applied Mathematics 010102 general mathematics Fibered knot 01 natural sciences Julia set law.invention 010101 applied mathematics Combinatorics Base (group theory) law Discrete Mathematics and Combinatorics 0101 mathematics Analysis Mathematics |
| Zdroj: | Discrete and Continuous Dynamical Systems. 36:5951-5970 |
| ISSN: | 1078-0947 |
| DOI: | 10.3934/dcds.2016061 |
| Popis: | In this work we define a stochastic adding machine associated to the Fibonacci base and to a probabilities sequence $\overline{p}=(p_i)_{i\geq 1}$. We obtain a Markov chain whose states are the set of nonnegative integers. We study probabilistic properties of this chain, such as transience and recurrence. We also prove that the spectrum associated to this Markov chain is connected to the fibered Julia sets for a class of endomorphisms in $\mathbb{C}^2$. |
| Databáze: | OpenAIRE |
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