Nonlinear Dynamics and Genome Analysis


Pedro Miramontes
Facultad de Ciencias
Universidad Nacional Autónoma de México



Early in the nineties, there was a boom of studies reporting
long-range fractal correlations in the DNA molecule. Since then, a
number of works reporting interesting DNA features using the language
and methods of Nonlinear Dynamics have been published.

In this presentation, we show that further analysis on genomes can be
carried out within the Dynamical Systems Theory framework. In
particular, we use the Poincaré Recurrence Theorem to detect repeated
non-periodic motifs along a genome and we extend the XOR multivariate
function to the domain of The Rational Numbers to map a genome into a
Sierpinsky Tetrahedron and extract genomic structural features that
tell appart different genomes.