Notes on the values of volume entropy of graphs

Kim, Woo-Yeon; Lim, Seonhee

doi:10.3934/dcds.2020221

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Translation Surfaces and Entropy2

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2022

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Cited by 2 publications

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“…There is a useful alternative formulation which we now present in the next lemma that follows from Definition 2.1 (see [11]).…”

Section: Translation Surfaces and Entropymentioning

confidence: 99%

Untitled

2022

Conform. Geom. Dyn.

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In this note we consider the entropy by Dankwart [On the largescale geometry of flat surfaces, 2014, PhD thesis. https://bib.math.unibonn.de/downloads/bms/BMS-401.pdf] of unit area translation surfaces in the SL(2, R) orbits of square tiled surfaces that are the union of squares, where the singularities occur at the vertices and the singularities have a common cone angle. We show that the entropy over such orbits is minimized at those surfaces tiled by equilateral triangles where the singularities occur precisely at the vertices. We also provide a method for approximating the entropy of surfaces in the orbits.

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“…There is a useful alternative formulation which we now present in the next lemma that follows from Definition 2.1 (see [11]).…”

Section: Translation Surfaces and Entropymentioning

confidence: 99%

Untitled

2022

Conform. Geom. Dyn.

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show abstract

“…There is a useful alternative formulation which we now present in the next lemma that follows from Definition 2.1 (see [11]).…”

Section: Translation Surfaces and Entropymentioning

confidence: 99%

Minimizing entropy for translation surfaces

Colognese¹,

Pollicott²

2022

Conform. Geom. Dyn.

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In this note we consider the entropy by Dankwart [On the large-scale geometry of flat surfaces, 2014, PhD thesis. https://bib.math.uni-bonn.de/downloads/bms/BMS-401.pdf] of unit area translation surfaces in the S L ( 2 , R ) SL(2, \mathbb R) orbits of square tiled surfaces that are the union of squares, where the singularities occur at the vertices and the singularities have a common cone angle. We show that the entropy over such orbits is minimized at those surfaces tiled by equilateral triangles where the singularities occur precisely at the vertices. We also provide a method for approximating the entropy of surfaces in the orbits.

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Notes on the values of volume entropy of graphs

Cited by 2 publications

References 14 publications

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Minimizing entropy for translation surfaces

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