Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.10209 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908877933510656 |
|---|---|
| author | Alves, Alexandre Miranda Gutiérrez, Gerardo Andrés Honorato Salarinoghabi, Mostafa |
| author_facet | Alves, Alexandre Miranda Gutiérrez, Gerardo Andrés Honorato Salarinoghabi, Mostafa |
| contents | In this work, we study the non-autonomous dynamics generated by random iterations of the cubic family of the form $z^3 + cz$. The parameter sequence is chosen randomly from a bounded Borel subset of $\mathbb{C}$. We investigate topological properties of the corresponding Julia sets, with particular emphasis on conditions leading to total disconnectedness. We prove that the set of parameter sequences for which the Julia set is totally disconnected is dense in the parameter space. We also construct examples where the Julia set is totally disconnected but the associated non-autonomous system is not hyperbolic. Finally, under suitable probabilistic assumptions on the parameter distribution, we show that almost every sequence produces a totally disconnected Julia set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10209 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Random Dynamics of a Family of Cubic Polynomials Alves, Alexandre Miranda Gutiérrez, Gerardo Andrés Honorato Salarinoghabi, Mostafa Dynamical Systems 30D05, 37F10, 37F12 In this work, we study the non-autonomous dynamics generated by random iterations of the cubic family of the form $z^3 + cz$. The parameter sequence is chosen randomly from a bounded Borel subset of $\mathbb{C}$. We investigate topological properties of the corresponding Julia sets, with particular emphasis on conditions leading to total disconnectedness. We prove that the set of parameter sequences for which the Julia set is totally disconnected is dense in the parameter space. We also construct examples where the Julia set is totally disconnected but the associated non-autonomous system is not hyperbolic. Finally, under suitable probabilistic assumptions on the parameter distribution, we show that almost every sequence produces a totally disconnected Julia set. |
| title | Random Dynamics of a Family of Cubic Polynomials |
| topic | Dynamical Systems 30D05, 37F10, 37F12 |
| url | https://arxiv.org/abs/2603.10209 |