Self-similar p-adic fractal strings and their complex dimensions

Research Articles

Abstract

We develop a geometric theory of self-similar p-adic fractal strings and their complex dimensions. We obtain a closed-form formula for the geometric zeta functions and show that these zeta functions are rational functions in an appropriate variable. We also prove that every self-similar p-adic fractal string is lattice. Finally, we define the notion of a nonarchimedean self-similar set and discuss its relationship with that of a self-similar p-adic fractal string. We illustrate the general theory by two simple examples, the nonarchimedean Cantor and Fibonacci strings.

Key words

fractal geometry p-adic analysis zeta functions complex dimensions self-similarity lattice strings and Minskowski dimension 

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaRiversideUSA
  2. 2.Department of MathematicsHawai‘i Pacific UniversityHonoluluUSA

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