Dynamics on Teichmüller Spaces and Self-covering of Riemann Surfaces

  title={Dynamics on Teichm{\"u}ller Spaces and Self-covering of Riemann Surfaces},
  author={EGE FUJIKAWA and Katsuhiko Matsuzaki and Masahiko Taniguchi},
A non-injective holomorphic self-cover of a Riemann surface induces a non-surjective holomorphic self-embedding of its Teichmüller space. We investigate the dynamics of such self-embeddings by applying our structure theorem of self-covering of Riemann surfaces and examine the distribution of its isometric vectors on the tangent bundle over the Teichmüller space. We also extend our observation to quasiregular self-covers of Riemann surfaces and give an answer to a certain problem on… CONTINUE READING

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