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Mathematics > Dynamical Systems

arXiv:2306.03611v4 (math)
[Submitted on 6 Jun 2023 (v1) , revised 13 Oct 2023 (this version, v4) , latest version 23 Jan 2024 (v8) ]

Title: Lyapunov Exponents for Open Billiard Flows

Title: 开放散射流的李雅普诺夫指数

Authors:Amal Al Dowais, Luchezar Stoyanov
Abstract: In this paper we prove that with respect to every ergodic invariant measure the positive Lyapunov exponents for the billiard flow in an open billiard in $\R^d$ ($d\geq 3$) are all equal. We should stress that we do not make any particular assumptions about the shape and size of the components of our obstacles -- they are just assumed to be strictly convex and compact with $C^3$ boundaries and satisfy the so called no eclipse condition.
Comments: There is a mistake in the proof of the Main Lemma 4.2
Subjects: Dynamical Systems (math.DS)
MSC classes: Primary: 37D20, 37D25, Secondary: 37D40
Cite as: arXiv:2306.03611 [math.DS]
  (or arXiv:2306.03611v4 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.2306.03611

Submission history

From: Luchezar Stoyanov [view email]
[v1] Tue, 6 Jun 2023 11:58:42 UTC (19 KB)
[v2] Thu, 8 Jun 2023 14:54:55 UTC (19 KB)
[v3] Wed, 11 Oct 2023 08:18:14 UTC (19 KB)
[v4] Fri, 13 Oct 2023 01:48:50 UTC (1 KB)
[v5] Wed, 22 Nov 2023 14:06:37 UTC (1 KB)
[v6] Sun, 17 Dec 2023 08:40:14 UTC (21 KB)
[v7] Tue, 19 Dec 2023 13:17:24 UTC (21 KB)
[v8] Tue, 23 Jan 2024 12:08:47 UTC (21 KB)
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