Journal of Modern Dynamics (JMD)

Global rigidity of certain Abelian actions by toral automorphisms

Pages: 425 - 442, Issue 3, July 2007      doi:10.3934/jmd.2007.1.425

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Federico Rodriguez Hertz - IMERL-Facultad de IngenierĂ­a, Universidad de la RepĂșblica, ulio Herrera y Reissig 565, CC 30, 11300 Montevideo, Uruguay (email)

Abstract: We prove global rigidity results for some linear abelian actions on tori. The type of actions we deal with includes in particular maximal rank semisimple actions on $\mathbb T^N$.

Keywords:  Anosov actions, rigidity, smooth conjugacy.
Mathematics Subject Classification:  Primary: 37C15, 37C85, 37D20; Secondary: 37D15, 37D25.

Received: June 2006;      Revised: March 2007;      Available Online: April 2007.