Fractal zeta functions of orbits of parabolic diffeomorphisms

  title={Fractal zeta functions of orbits of parabolic diffeomorphisms},
  author={P. Marde{\vs}i{\'c} and Goran Radunovi'c and Maja Resman},
  journal={Analysis and Mathematical Physics},
In this paper, we prove that fractal zeta functions of orbits of parabolic germs of diffeomorphisms can be meromorphically extended to the whole complex plane. We describe their set of poles (i.e. their complex dimensions) and their principal parts which can be understood as their fractal footprint. We study the fractal footprint of one orbit of a parabolic germ f and extract intrinsic information about the germ f from it, in particular, its formal class. Moreover, we relate complex dimensions… 

Reading analytic invariants of parabolic diffeomorphisms from their orbits

. In this paper we study germs of diffeomorphisms in the complex plane. We address the following problem: How to read a diffeomorphism f knowing one of its orbits A ? We solve this problem for



Introduction to analytic number theory

This is the first volume of a two-volume textbook which evolved from a course (Mathematics 160) offered at the California Institute of Technology during the last 25 years. It provides an introduction

Fractal Zeta Functions and Fractal Drums: Higher-Dimensional Theory of Complex Dimensions

Recently, the first author has extended the definition of the zeta function associated with fractal strings to arbitrary bounded subsets $A$ of the $N$-dimensional Euclidean space ${; ; \mathbb R}; ;

Tubular neighborhoods of orbits of Dulac maps

  • J. Dyn. Differ. Equ. 1, 1–49
  • 2019

Epsilon-neighborhoods of orbits and formal classification of parabolic diffeomorphisms

In this article we study the dynamics generated by germs of parabolic diffeomorphisms f : (C; 0)->(C; 0) tangent to the identity. We show how formal classification of a given parabolic diffeomorphism

Essential singularities of fractal zeta functions

We study the essential singularities of geometric zeta functions $\zeta_{\mathcal L}$, associated with bounded fractal strings $\mathcal L$. For any three prescribed real numbers $D_{\infty}$, $D_1$


  • Show Me Small-Town Missouri
  • 2020

Hyperbolic systems

Complex dynamics

The politics of bovine TB is obviously complex, as the past few weeks have demonstrated, but so too is the science – and not just in relation to badgers. Two recently published papers highlight the