Livsic Theorem for cocycles with value in Gl(n,Q_p)
Open Access
Author:
Zhu, Lin
Graduate Program:
Mathematics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 22, 2012
Committee Members:
Anatole Katok, Dissertation Advisor/Co-Advisor Manfred Heinz Denker, Committee Member Federico Rodriguez Hertz, Committee Member Sencun Zhu, Committee Member
Keywords:
Livsic theorem p-adic field dynamical systems
Abstract:
We extend the well-known results of Liv\v{s}ic theorem on the regularity of measurable solutions to GL(n,Q_p) valued cocycles, where Q_p is the p-adic field, which is a non-archimedean field. To prove the main result, we give the approximation of Lyapunove exponents by the Lyapunov exponents at periodic points and prove the uniformly boundedness of the cocycle if it is uniformly bounded at periodic points under the non-archimedean condition.
