I am mainly interested in mathematical problems involving computations in continuous spaces where analytical, geometrical, dynamical and computational complexity properties interact in non trivial ways.

- How to lose at Monte Carlo: a simple dynamical system whose typical statistical behavior is non computable.
. Accepted to STOC 2020. e-print ArXiv:1910.09625

with M. Yampolsky - Real quadratic Julia sets can have arbitrarily high complexity
. Accepted to J. Found. Comp. Math. e-print ArXiv:1904.06204

with M. Yampolsky - Computability of topological entropy: From general systems to transformations on Cantor sets and the interval
. Accepted to Disc. Cont. Dyn. Sys. A. e-print ArXiv:1906.01745

with S. Gangloff, A. Herrera and M. Sablik. - Computational Intractability of attractors in the real quadratic family
Adv. in Math. Volume 349, pp: 941-958, 2019. e-print ArXiv:1703.04660

with M. Yampolsky. - Computability on quasi-Polish spaces
Descriptive Complexity of Formal Systems (DCFS) 2019. e-print ArXiv:1903.02979

with M. Hoyrup, V. Selivanov and D. Stull. - Non Computable Mandelbrot-like sets for a one parameter quadratic family
Inf. and Comp. Volume 262, pp: 110-122, 2018. e-print ArXiv:1703.04668

with D. Coronel and M. Yampolsky. - Caratheodory Convergence and Harmonic Measure
Potential Analysis. pp: 1-11, 2018. e-print ArXiv:1805.08821

with I. Binder and M. Yampolsky. - Computing geometric Lorenz attractors with arbitrary precision
*with D. Graca and N. Zhong.*Trans. Am. Math. Soc. 370 (2018), 2955-2970. e-print ArXiv:1702.04059. - Tight Space-Noise tradeoff in computing the ergodic measure
. Sbornik: Mathematics, Volume 208, Number 12. 2017. e-print ArXiv:1508.05372

with M. Braverman and J. Schneider - On the information carried by programs about the objects they compute
*with M. Hoyrup*. STACS 2015 and Theo. Comp. Sys. Volume 61, Issue 4, pp 1214-1236, 2017. e-print ArXiv:1409.6977 - Space Bounded Church-Turing thesis and computational tractability of closed systems
*with M. Braverman and J. Scheiner.*Phys. Rev. Lett. 115, 098701. 2015. e-print Arxiv:1905.03610 - Non-computable impressions of computable rays of quadratic polynomials
*with I. Binder and M. Yampolsky.*Commun. Math. Phys. (2015) 335: 739. e-print ArXiv:1402.0440. - Computable Caratheodory theory
*with I. Binder and M. Yampolsky.*Adv. in Math. Volume 265, pp:280-312, 2014. e-print ArXiv:1209.6096. - Probability, Statistics and computation in dynamical systemes
*with S. Galatolo and I. Nisoli.*Math. Struct. in Comp. Sci. Volume 24, Special Issue 03, June 2014. - Schnoor Randomness and the Lebesgue Differentiation Theorem
*with N. Pathak and S. Simpson*. Proc. Am. Math. Soc. Volume 142, Number 1, January 2014. - Statistical properties of dynamical systems - Simulation and abstract computation
*with M. Hoyrup and S. Galatolo.*Chaos, Solitons & Fractals, Volume 45, Issue 1, 2013, pp: 1-14. pdf. - Noise vs Computational intractability in dynamics
*with M. Braverman and A. Grigo*. Innovations in Theoretival Computer Science (ITCS) 2012. pdf. e-print ArXiv:1201.0488. - Computability of the Radon-Nikodym derivative
*with M. Hoyrup and K. Weihrauch*. Computability, Volume 1, Issue 1, 2012, pp: 1-13. -pdf. - Algorithmic tests and randomness with respect to a class of measures
*with L. Bienvenue, P. Gács, M. Hoyrup and A. Shen.*Proc. Steklov Inst. Math., 274(1):34-89. pdf - Computability of the Brolin-Lyubich measure
*with M. Braverman, I. Binder and M. Yampolsky.*Commun. Math. Phys. 335(3), Dec. 2011, pp 743-771. pdf - Computability of the Radon Nikodym derivative

*with M. Hoyrup and K. Weihrauch*. CiE 2011. pdf - Discretization of continuous functions. Some typical properties

*with S. Troubetzkoy.*Discrete Mathematics. Volume 311, Issues 8-9, 6 May 2011, pp: 620-627. pdf - Dynamics and abstract computability: Computing Invariant Measures

*with S. Galatolo and M. Hoyrup.*Disc. Cont. Dyn. Syst. Series A. Volume: 29, issue: 1, 2011. pp: 193 - 212. pdf. - Randomness on Computable Probability Spaces. A Dynamical Point of View

with P. Gács and M. Hoyrup Theo. Comp. Sys. Volume 48, Number 3, pp: 465-485, 2011. pdf. - Computing the speed of convergence of ergodic averages and pseudorandom points in dynamical systems

with S. Galatolo and M. Hoyrup - Effective symbolic dynamics, random points, statistical behavior, complexity and entropy
Information and Computation. 208(1): 23-41, 2010 pdf

with S. Galatolo and M. Hoyrup. - Computability of probability measures and Martin-Löf randomness over metric spaces
*with M. Hoyrup*. Information and Computation. 207(7):830-847, 2009.pdf - A Constructive Borel-Cantelli lemma: constructing orbits with required statistical properties
Theo. Comp. Sci. 410(21-23):2207-2222, 2009. pdf

with S. Galatolo and M. Hoyrup. - Randomness on Computable Probability Spaces. A Dynamical Point of View
*with P. Gács and M. Hoyrup*. STACS 2009. pdf - An Application of Martin-Löf Randomness to Effective Probability Theory: Layerwise Computability
*with M. Hoyrup.*CiE 2009. LNCS, 5635:260-269, 2009. pdf - Applications of Effective Probablity Theory to Martin Löf Randomness
*with M. Hoyrup.*ICALP 2009. LNCS, 5555:549-561, 2009. pdf. - Computability and Information in models of Randomness and Chaos

Math. Struc. Comp. Sci., vol. 18, pp 291-307, 2008. pdf

- Computable geometric complex analysis and complex dynamics
. e-print ArXiv:1703.06459

with M. Yampolsky - Absolute continuity of measures and preservation of Randomness
*with Hoyrup.*pdf

A short introduction to computability in euclidean space with applications. pdf

Randomness and Ergodic Theory: an Algorithmic point of view. Phd Thesis. pdf