Topological Entropy Of The Linear Map On Q_p~m

There are just, essentially, two different metrics: one is Archimedean metric, i.e. general absolute value metric, while, the other is non-Archimedean metric, i.e. p-adic metric. The completion of Q under those two different metrics are the field R of the real numbers and Q_p of p-adic numbers.Analysis of the field Q_p is very important to study number theory, representation of Lie-Groups and theoretical physical.It has been more than 100 years since Poincare introduced dynamical systems under Archimedean metric in. In resent years, when the need of studying number theory, theoretical physical and intelligent arises, more eyes rely on dynamical systems on p-adic spaces. Due to non-Archimedean of p-adic metric, these systems have many interesting properties that different from those of the real numbers.This essay studied topological entropy of the linear map T : Q_p~m→Q_p~m, and getwhile a_i∈C_p are eigenvalues of T.Even if the result is similar to the linear map of R~m, but the art of the certification is different. Compare to the real case, this certification is more brief and direct.