New loxodromic elements found in infinite-type surfaces.
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5 results for “Thurston-Veech”
problem Finding loxodromic elements in infinite-type surfaces.
method Adapting Thurston-Veech construction for infinite-type surfaces.
result Infinitely many loxodromic elements produced without leaving finite-type subsurfaces invariant.
Proves even degrees can be realized in Abelian differential strata.
problem Realizing even degrees as stretch factors in Abelian differentials.
method Analyzes Thurston-Veech stretch factors in moduli spaces.
result Every even degree is realized in Abelian differentials.
The study finds all trace field degrees for Torelli group mappings.
problem Identifying all possible trace field degrees for Torelli group mappings.
method Using Thurston-Veech construction of pseudo-Anosov maps, and providing examples of stretch factors with specific algebraic degrees.
result All integers are trace field degrees for .
In this paper we are interested in the stratum H^{hyp}(4) of translation surfaces, which consists of pairs (M,ω), where M is a hyper-elliptic Riemann surface of genus 3, and ωis a holopmorphic 1-form on M having only one zero. We first show that every surface in this stratum can be decomposed into parallelograms follow…
Book explores infinite translation surfaces, challenging traditional geometry.
problem Understanding infinite-type translation surfaces.
method Detailed classification, construction, and analysis of symmetries.
result Complex dynamics in infinite-type translation flows.