Research

My research concerns random and non-autonomous dynamical systems. I am particularly interested in the areas of thermodynamic formalism, fractal geometry, transcendental dynamics, holomorphic dynamics, conformal dynamics, open dynamical systems, ergodic theory, extreme value theory, and iterated function systems.

Books:

• [Arxiv] – with H. Sumi, M. Urbanski: The Dynamics and Geometry of Semi-Hyperbolic Rational Semigroups. To appear in Memoirs of the American Mathematical Society.
• [Arxiv] – with G. Froyland, C. Gonzalez-Tokman, S. Vaienti: Thermodynamic Formalism and Perturbation Formulae for Quenched Random Dynamical Systems. To appear in Dissertationes Mathematicae. – This monograph is a combination and update of the following two preprints:
  • [Arxiv] – with G. Froyland, C. Gonzalez-Tokman, S. Vaienti: Thermodynamic Formalism for Random Interval Maps with Holes.
  • [Arxiv] – with G. Froyland, C. Gonzalez-Tokman, S. Vaienti: Perturbation formulae for quenched random dynamics with application to open systems and extreme value theory.

Journal Publications:

• [Arxiv] [Journal] – with G. Froyland, C. Gonzalez-Tokman, S. Vaienti: Equilibrium States for Non-Transitive Random Open and Closed Dynamical Systems. Ergodic Theory and Dynamical Systems. (2022).
• [Arxiv] [Journal] – with G. Froyland, C. Gonzalez-Tokman, S. Vaienti: Thermodynamic Formalism for Random Weighted Covering Systems. Commun. Math. Phys. (2021).
• [Arxiv] [Journal] –  with M. Urbanski: Critically Finite Random Maps of an Interval. Discrete & Continuous Dynamical Systems – A, 40(8):4839, 2020.
  

Preprints:

• [Arxiv] – with G. Froyland, Peter Koltai: An inflated dynamic Laplacian to track the emergence and disappearance of semi-material coherent sets.
• [Arxiv] – with G. Froyland, C. Gonzalez-Tokman, A. Quas: Universal Gap Growth for Lyapunov Exponents of Perturbed Matrix Products.
• [Arxiv] – with G. Froyland, C. Gonzalez-Tokman, S. Vaienti: Compound Poisson statistics for dynamical systems via spectral perturbation.
• [Arxiv]  – with N. Haydn, S. Vaienti: Extreme Value Theory with Spectral Techniques: application to a simple attractor.
  
• [Arxiv] – with M.K. Roychowdhury, M. Urbanski: Quantization dimension for infinite conformal iterated function systems.
• [Arxiv] –  Dimensions of non-autonomous meromorphic functions of finite order.
• [Arxiv] –  Non-Autonomous Conformal Graph Directed Markov Systems.
• [Arxiv] –  An Almost Sure Invariance Principle for Several Classes of Random Dynamical Systems.