Negative Lyapunov exponent of circle maps forced by expanding circle endomorphisms
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912559029813248 |
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| author | Rajasekar, Kirthana |
| author_facet | Rajasekar, Kirthana |
| contents | We study maps on the torus $\mathbb{T}^2$ that are of the form $F(x,y) = (bx, f_x(y))$, where $b\geq 2$ is an integer. We establish an open class of $C^1$-maps, with $f_x(y)$ that are typically non-monotonic in $x$, for which the Lyapunov exponents on the fibre are negative almost everywhere. For each fixed $f_x(y)$ and a base map $bx$ that is sufficiently expanding, we establish a uniform upper bound for the Lyapunov exponents; moreover, the uniform bound depends on selective characteristics of $f$. This implies that orbits on the same fibre exhibit local synchronisation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21645 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Negative Lyapunov exponent of circle maps forced by expanding circle endomorphisms Rajasekar, Kirthana Dynamical Systems 37E10, 37D25 We study maps on the torus $\mathbb{T}^2$ that are of the form $F(x,y) = (bx, f_x(y))$, where $b\geq 2$ is an integer. We establish an open class of $C^1$-maps, with $f_x(y)$ that are typically non-monotonic in $x$, for which the Lyapunov exponents on the fibre are negative almost everywhere. For each fixed $f_x(y)$ and a base map $bx$ that is sufficiently expanding, we establish a uniform upper bound for the Lyapunov exponents; moreover, the uniform bound depends on selective characteristics of $f$. This implies that orbits on the same fibre exhibit local synchronisation. |
| title | Negative Lyapunov exponent of circle maps forced by expanding circle endomorphisms |
| topic | Dynamical Systems 37E10, 37D25 |
| url | https://arxiv.org/abs/2508.21645 |