Stefano Galatolo

Effective symbolic dynamics, random points, statistical behavior, complexity and entropy

We consider the dynamical behavior of Martin-Lof random points in dynamical systems over metric spaces with a computable dynamics and a computable invariant measure. We use computable partitions to define a sort of effective symbolic model for the dynamics. Through this construction, we prove that such points have typical statistical behavior (the behavior which is typical in the Birkhoff ergodic theorem) and are recurrent. We introduce and compare some notions of complexity for orbits in dynamical systems and prove: (i) that the complexity of the orbits of random points equals the Kolmogorov-Sinai entropy of the system, (ii) that the supremum of the complexity of orbits equals the topological entropy.

Lorenz-like flows: exponential decay of correlations for the Poincaré map, logarithm law, quantitative recurrence

In this paper we prove that the Poincare map associated to a Lorenz like flow has exponential decay of correlations with respect to Lipschitz observables. This implies that the hitting time associated to the flow satisfies a logarithm law. The hitting time

Recurrence and algorithmic information

tau_r(x,x_0)

A constructive Borel-Cantelli lemma. Constructing orbits with required statistical properties

is the time needed for the orbit of a point

Textile-Based Electrogoniometers for Wearable Posture and Gesture Capture Systems

x

Orbit complexity by computable structures

to enter for the first time in a ball

Information and dynamical systems: a concrete measurement on sporadic dynamics

B_r(x_0)

Complexity, initial condition sensitivity, dimension and weak chaos in dynamical systems

centered at

Modeling and Characterization of Extensible Wearable Textile-Based Electrogoniometers

x_0

An Elementary Approach to Rigorous Approximation of Invariant Measures

, with small radius