Dynamical Systems (especially Symbolic Dynamics, Iterated Functions Systems and Graph Directed Markov Systems)
Ergodic Theory
Thermodynamic Formalism
Fractal Geometry

Doctorate:
University of Goettingen, Advisor: Manfred Denker
Masters:
Laval University, Advisor: Thomas J. Ransford

Books

1. Noninvertible Dynamical Systems - Volume 1: Ergodic Theory - Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps, De Gruyter Expositions in Mathematics 69/1, 2021, with Sara Munday (John Cabot University) and Mariusz Urbanski (University of North Texas).

2. Noninvertible Dynamical Systems - Volume 2: Finer Thermodynamic Formalism, Distance Expanding Maps and Countable State Subshifts of Finite Type, Conformal GDMSs, Lasota-Yorke Maps and Fractal Geometry, De Gruyter Expositions in Mathematics 69/2, 2022, with Sara Munday (John Cabot University) and Mariusz Urbanski (University of North Texas).

3. Noninvertible Dynamical Systems - Volume 3: Analytic Endomorphisms of the Riemann Sphere, De Gruyter Expositions in Mathematics 69/3, 2023, with Sara Munday (John Cabot University) and Mariusz Urbanski (University of North Texas).

Journal Articles

Most recent

1. The Hausdorff dimension spectrum of conformal graph directed Markov systems and applications to nearest integer continued fractions (with Andrei Ghenciu, University of Wisconsin, and Sara Munday, John Cabot University), Journal of Number Theory, 175 (2017), 223–249.

2. Conformal graph directed Markov systems: beyond finite irreducibility (with Andrei Ghenciu, University of Wisconsin, andDan Mauldin, University of North Texas), Journal of Fractal Geometry, 3 (3) (2016), 217–243.

3. Bowen’s formula for shift-generated finite conformal recursive constructions (with Andrei Ghenciu, University of Wisconsin), Real Analysis Exchange, 40 (1) (2015), 99–112.

4. Gibbs states for non-irreducible countable Markov shifts (with Andrei Ghenciu, University of Wisconsin), Fundamenta Mathematicae, 221 (3) (2013), 231–265.

5. A new variation of Bowen’s formula for graph directed Markov systems, Discrete and Continuous Dynamical Systems — Series A, 32 (7) (2012), 2533–2551.

My Erdòs number is 2.

Deutsch (German)