Coexistence of two contrasting recurrence properties of certain non-integrable cocycles
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908783442132992 |
|---|---|
| author | Berk, Przemysław Kotlewski, Łukasz |
| author_facet | Berk, Przemysław Kotlewski, Łukasz |
| contents | We study the recurrence properties of certain skew products over symmetric interval exchange transformations, including rotations, with cocycles of the form $f(x)=-\frac{1}{x^a}+\frac{1}{(1-x)^a}$, where $a>1$. We prove that typically, such systems are dissipative. However, at the same time they are \emph{topologically recurrent}, i.e. for every open rectangle $A\subset[0,1)\times \R$, there exists an infinite sequence $(q_n)_{n=1}^{\infty}$ such that $T^{q_n}_f(A)\cap A\neq\emptyset$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16701 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coexistence of two contrasting recurrence properties of certain non-integrable cocycles Berk, Przemysław Kotlewski, Łukasz Dynamical Systems 37A40, 37E05 We study the recurrence properties of certain skew products over symmetric interval exchange transformations, including rotations, with cocycles of the form $f(x)=-\frac{1}{x^a}+\frac{1}{(1-x)^a}$, where $a>1$. We prove that typically, such systems are dissipative. However, at the same time they are \emph{topologically recurrent}, i.e. for every open rectangle $A\subset[0,1)\times \R$, there exists an infinite sequence $(q_n)_{n=1}^{\infty}$ such that $T^{q_n}_f(A)\cap A\neq\emptyset$. |
| title | Coexistence of two contrasting recurrence properties of certain non-integrable cocycles |
| topic | Dynamical Systems 37A40, 37E05 |
| url | https://arxiv.org/abs/2601.16701 |