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.

Published / accepted

How to lose at Monte Carlo: a simple dynamical system whose typical statistical behavior is non computable.
with M. Yampolsky. Accepted to STOC 2020. e-print ArXiv:1910.09625
Real quadratic Julia sets can have arbitrarily high complexity
with M. Yampolsky. Accepted to J. Found. Comp. Math. e-print ArXiv:1904.06204
Computability of topological entropy: From general systems to transformations on Cantor sets and the interval
with S. Gangloff, A. Herrera and M. Sablik.. Accepted to Disc. Cont. Dyn. Sys. A. e-print ArXiv:1906.01745
Computational Intractability of attractors in the real quadratic family
with M. Yampolsky. Adv. in Math. Volume 349, pp: 941-958, 2019. e-print ArXiv:1703.04660
Computability on quasi-Polish spaces
with M. Hoyrup, V. Selivanov and D. Stull. Descriptive Complexity of Formal Systems (DCFS) 2019. e-print ArXiv:1903.02979
Non Computable Mandelbrot-like sets for a one parameter quadratic family
with D. Coronel and M. Yampolsky. Inf. and Comp. Volume 262, pp: 110-122, 2018. e-print ArXiv:1703.04668
Caratheodory Convergence and Harmonic Measure
with I. Binder and M. Yampolsky. Potential Analysis. pp: 1-11, 2018. e-print ArXiv:1805.08821
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
with M. Braverman and J. Schneider. Sbornik: Mathematics, Volume 208, Number 12. 2017. e-print ArXiv:1508.05372
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. CCA 2010. Computability and Complexity in Analysis. pdf.
Effective symbolic dynamics, random points, statistical behavior, complexity and entropy
with S. Galatolo and M. Hoyrup. Information and Computation. 208(1): 23-41, 2010 pdf
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
with S. Galatolo and M. Hoyrup. Theo. Comp. Sci. 410(21-23):2207-2222, 2009. pdf
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

Preprints

Computable geometric complex analysis and complex dynamics
with M. Yampolsky. e-print ArXiv:1703.06459
Absolute continuity of measures and preservation of Randomness
with Hoyrup. pdf

Other

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

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

Program size complexity of self assembled shapes in Winfree's model. Master thesis. Tesis (in spanish), paper (in english).

Cristobal Rojas's Publications

Research interest

Published / accepted

Preprints

Other

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