Zero Lyapunov Exponents in Transitive Skew-products of Iterated Function Systems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917416403992576 |
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| author | Barrientos, Pablo G. Cisneros, Joel Angel |
| author_facet | Barrientos, Pablo G. Cisneros, Joel Angel |
| contents | We study the class of transitive skew-products associated with iterated function systems of circle diffeomorphisms. We can approximate any transitive skew-product by maps in this class that have a robustly zero Lyapunov exponent. In particular, we prove the existence of non-hyperbolic ergodic measures for an open and dense subset of transitive skew-products. Moreover, these measures have full support and are the weak$^*$ limit of periodic measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11040 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zero Lyapunov Exponents in Transitive Skew-products of Iterated Function Systems Barrientos, Pablo G. Cisneros, Joel Angel Dynamical Systems We study the class of transitive skew-products associated with iterated function systems of circle diffeomorphisms. We can approximate any transitive skew-product by maps in this class that have a robustly zero Lyapunov exponent. In particular, we prove the existence of non-hyperbolic ergodic measures for an open and dense subset of transitive skew-products. Moreover, these measures have full support and are the weak$^*$ limit of periodic measures. |
| title | Zero Lyapunov Exponents in Transitive Skew-products of Iterated Function Systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2403.11040 |