22 citations · 57 across the 23 of their papers we have counts for
12 papers · 1 filter
On the algorithmic descriptive complexity of attractors in topological dynamics
Cristobal Rojas, Mathieu Sablik
We study the computational problem of rigorously describing the asymptotic behaviour of topological dynamical systems up to a finite but arbitrarily small pre-specified error. More…
How to lose at Monte Carlo: a simple dynamical system whose typical statistical behavior is non computable
Cristobal Rojas, Michael Yampolsky
We consider the simplest non-linear discrete dynamical systems, given by the logistic maps of the interval . We show that there exist real parameters $a\i…
On the computability properties of topological entropy: a general approach
Silvere Gangloff, Alonso Herrera, Cristobal Rojas +1
The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, th…
Real quadratic Julia sets can have arbitrarily high complexity
Cristobal Rojas, Michael Yampolsky
We show that there exist real parameters for which the Julia set of the quadratic map has arbitrarily high computational complexity. More precisely, we show that…
Computational intractability of attractors in the real quadratic family
Cristobal Rojas, Michael Yampolsky
We show that there exist real quadratic maps of the interval whose attractors are computationally intractable. This is the first known class of such natural examples.
Computing geometric Lorenz attractors with arbitrary precision
Daniel Graca, Cristobal Rojas, Ning Zhong
The Lorenz attractor was introduced in 1963 by E. N. Lorenz as one of the first examples of \emph{strange attractors}. However Lorenz' research was mainly based on (non-rigourous)…
Non-computable impressions of computable external rays of quadratic polynomials
Ilia Binder, Cristobal Rojas, Michael Yampolsky
We discuss computability of impressions of prime ends of compact sets. In particular, we construct quadratic Julia sets which possess explicitly described non-computable impression…
Dynamical systems, simulation, abstract computation
Stefano Galatolo, Mathieu Hoyrup, Cristóbal Rojas
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantitie…
Computability of Brolin-Lyubich Measure
Ilia Binder, Mark Braverman, Cristobal Rojas +1
Brolin-Lyubich measure of a rational endomorphism $R:\riem\to\riem$ with is the unique invariant measure of maximal entropy . Its…
Coding discretizations of continuous functions
Cristobal Rojas, Serge Troubetzkoy
We consider several coding discretizations of continuous functions which reflect their variation at some given precision. We study certain statistical and combinatorial properties…
Dynamics and abstract computability: computing invariant measures
Stefano Galatolo, Mathieu Hoyrup, Cristobal Rojas
We consider the question of computing invariant measures from an abstract point of view. We work in a general framework (computable metric spaces, computable measures and functions…
Effective symbolic dynamics, random points, statistical behavior, complexity and entropy
Stefano Galatolo, Mathieu Hoyrup, Cristobal Rojas
We consider the dynamical behavior of Martin-Löf random points in dynamical systems over metric spaces with a computable dynamics and a computable invariant measure. We use computa…