Journal of Modern Dynamics (JMD)

Infinitely many lattice surfaces with special pseudo-Anosov maps

Pages: 239 - 254, Issue 2, June 2013      doi:10.3934/jmd.2013.7.239

       Abstract        References        Full Text (203.7K)       Related Articles       

Kariane Calta - Vassar College, Poughkeepsie, NY 12604-0257, United States (email)
Thomas A. Schmidt - Oregon State University, Corvallis, OR 97331, United States (email)

Abstract: 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.

Keywords:  Pseudo-Anosov, SAF invariant, flux, translation surface, Veech group.
Mathematics Subject Classification:  Primary: 37D99; Secondary: 30F60, 37A25, 37A45, 37F99, 58F15.

Received: October 2012;      Revised: May 2013;      Available Online: September 2013.