Computation of symbolic dynamics for one-dimensional maps

Symbolic Dynamics of One-Dimensional Maps: Entropies, Finite Precision, and Noise

In the study of nonlinear physical systems, one encounters apparently random or chaotic behavior, although the systems may be completely deterministic. Applying techniques from symbolic dynamics to maps of the interval, we compute two measures of chaotic behavior commonly employed in dynamical systems theory: the topological and metric entropies. For the quadratic logistic equation, we find tha...

Symbolic dynamics for Lozi maps

We study the family of the Lozi maps La,b : R2 → R2, La,b(x, y) = (1+y−a|x|, bx), and their strange attractors Λa,b. We introduce the set of kneading sequences for the Lozi map and prove that it determines the symbolic dynamics for that map. We also introduce two other equivalent approaches. 2010 Mathematics Subject Classification: 37B10, 37D45, 37E30, 54H20

Symbolic computation of the Duggal transform

Following the results of cite{Med}, regarding the Aluthge transform of polynomial matrices, the symbolic computation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical charac...

Induced Maps , Markov Extensions and Invariantmeasures in One - Dimensional Dynamics

PUZZLES OF QUASI-FINITE TYPE, ZETA FUNCTIONS AND SYMBOLIC DYNAMICS FOR MULTI-DIMENSIONAL MAPS by