arXiv subjects

Hamid Naderiyan

Publications and source records attributed to Hamid Naderiyan.

3 recordsLinked to original sources

arXiv2025

Thermodynamic Formalism for a Class of Hyperbolic Transcendental Meromorphic Functions

This paper studies the thermodynamic formalism in the context of complex dynamics. We establish the thermodynamics formalism for the class of hyperbolic transcendental meromorphic functions of B-class, where the poles have bounded multiplicities, the Nevanlinna order is finite, and infinity is not an asymptotic value. We showed the existence and uniqueness of the conformal measure and the invariant Gibbs measure equivalent to the conformal measure.

math.DS↗

arXiv2024

Counting Problem for Some Random Conformal Iterated Function Systems

This paper studies the counting problem in random dynamical systems. We noticed that the nature of counting in the random setting is completely different than that of the deterministic systems in the sense that non-exponential growth is constructed on a set of full measure. The recurrent behavior of random walks plays a major role in counting in the random setting.

math.DS↗

arXiv2024

Improved Bounds For Some Asymptotic Formulas for Counting Words in Shift Spaces

This paper studies a version of the counting problem in dynamical systems that is of interest, especially in conformal dynamical systems where the functions of the systems are angle preserving. Recently, M. Pollicott and M. Urbański published a result in this context for D-generic systems where the complex transfer operator behaves nicely on the critical line of the Poincaré series. Their result contains an asymptotic formula for the Apollonian circle packing. We lift the D-generic condition and conformality of the functions system in this paper to see how their asymptotic formula changes. We use some recent Tauberian theorem to show that the formula gets a form whose limit infimum and limit supremum bounds can be obtained in the sharpest sense. Further, we observed an asymptotic of length closely related to this counting problem. In fact, not only the number of words is subject to some formula, but also their length as well.

math.DS↗