Abstract
In this thesis, we investigate the largest Lyapunov exponent for open billiards in both two- and higherdimensional
Euclidean spaces. In $\mathbb{R}^2$, we estimate the largest Lyapunov exponent
$\lambda_1$ for open billiards, demonstrating its continuity and differentiability with respect to a
small perturbation parameter $\alpha$. Extending this investigation to $\mathbb{R}^n$ for $n\geq3$,
we prove similar results for the largest Lyapunov exponent in higher dimensions. Additionally, we
consider the billiard flow in the exterior of at least three balls in $\mathbb{R}^3$, assuming the noeclipse
condition (H) and small radii. We prove that the two positive Lyapunov exponents are
different: $\lambda_1>\lambda-2>0$.
Euclidean spaces. In $\mathbb{R}^2$, we estimate the largest Lyapunov exponent
$\lambda_1$ for open billiards, demonstrating its continuity and differentiability with respect to a
small perturbation parameter $\alpha$. Extending this investigation to $\mathbb{R}^n$ for $n\geq3$,
we prove similar results for the largest Lyapunov exponent in higher dimensions. Additionally, we
consider the billiard flow in the exterior of at least three balls in $\mathbb{R}^3$, assuming the noeclipse
condition (H) and small radii. We prove that the two positive Lyapunov exponents are
different: $\lambda_1>\lambda-2>0$.
| Original language | English |
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| Qualification | Doctor of Philosophy |
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| Supervisors/Advisors |
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| Award date | 31 Jan 2025 |
| DOIs | |
| Publication status | Unpublished - 2025 |