## Journals

- Advances in Mathematics of Communications
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- Discrete & Continuous Dynamical Systems - A
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- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Foundations of Data Science
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- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
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- Journal of Modern Dynamics
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- AIMS Mathematics
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### Open Access Journals

JMD

We develop an algebraic framework for studying translation surfaces. We
study the Sah--Arnoux--Fathi-invariant and the collection of directions in
which it vanishes. We show that these directions are described by a number
field which we call the periodic direction field. We study the
$J$-invariant of a translation surface, introduced by Kenyon and Smillie
and used by Calta. We relate the $J$-invariant to the periodic direction
field. For every number field $K\subset\ \mathbb R$ we show that there is a
translation surface for which the periodic direction field is $K$. We study
automorphism groups associated to a translation surface and relate them to
the $J$-invariant. We relate the existence of decompositions of translation
surfaces into squares with the total reality of the periodic direction
field.

JMD

We give explicit pseudo-Anosov homeomorphisms with vanishing
Sah-Arnoux-Fathi invariant. Any translation surface whose Veech group
is commensurable to any of a large class of triangle groups is shown
to have an affine pseudo-Anosov homeomorphism of this type. We also
apply a reduction to finite triangle groups and thereby show the
existence of nonparabolic elements in the periodic field of certain
translation surfaces.

## Year of publication

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