Generalized Sturmian languages

Lopez, Luis-Miguel; Narbel, Philippe

doi:10.1007/3-540-60084-1_86

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2018

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Cited by 5 publications

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“…[Joh17]. Beyond the Veech case, there is a long string of papers of Lopez-Narbel developing a language-theoretic formulation of generalized Sturmian sequences for interval exchange transformations, beginning with [LN95].…”

Section: Introductionmentioning

confidence: 99%

You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces

Duchin¹,

Erlandsson²,

Leininger³

et al. 2018

Preprint

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We give a complete characterization of the relationship between the shape of a Euclidean polygon and the symbolic dynamics of its billiard flow. We prove that the only pairs of tables that can have the same bounce spectrum are right-angled tables that differ by an affine map. The main tool is a new theorem that establishes that a flat cone metric is completely determined by the support of its Liouville current.

show abstract

Section: Introductionmentioning

confidence: 99%

You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces

Duchin¹,

Erlandsson²,

Leininger³

et al. 2018

Preprint

View full text Add to dashboard Cite

show abstract

“…For example, in Section 4 we sketch a similar result for cutting sequences. the Veech case, there is a long string of papers of Lopez-Narbel developing a language-theoretic formulation of generalized Sturmian sequences for interval exchange transformations, beginning with [LN95].…”

Section: Introductionmentioning

confidence: 99%