Fractality and Lapidus zeta functions at infinity

Abstract

We study fractality of unbounded sets of finite Lebesgue measure at infinity by introducing the notions of Minkowski dimension and content at infinity. We also introduce the Lapidus zeta function at infinity, study its properties and demonstrate its use in analysis of fractal properties of unbounded sets at infinity.

19 pages, 1 figure

References in corpus (1)

• Fractal Zeta Functions and Complex Dimensions of Relative Fractal Drums

Cited by in corpus (2)

• Complex dimensions of fractals and meromorphic extensions of fractal zeta functions
• Minkowski measurability criteria for compact sets and relative fractal drums in Euclidean spaces