Linear difference equations over p-adic and finite fields

Details Linear difference equations over p-adic and finite fields Linear difference equations over p-adic and finite fields

2010-03-26

arxiv.org/abs/1003.5028v1

Mathematics

Dynamical Systems

Scientific paper

First, we study p-adic matrices and their discrete dynamics over p-adic
numbers C_p. We prove that if p-adic absolute value of every eigenvalue of a
p-adic matrix is less than 1 then every solution of v_{n+1}=Av_n converges to 0
as n tends to infinity. Second, we study the periodicity of solutions of the
system over finite fields.

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