IJPAM: Volume 10, No. 4 (2004)

KNEADING THEORY FOR TRIANGULAR MAPS

Diana Aldea Mendes$^{1}$, José Sousa Ramos$^{2}$
$^1$Department of Quantitative Methods
ISCTE - Superior Institute of Labour and Management Science
Avenida das Forças Armadas
1649-026 Lisbon, PORTUGAL
e-mail: diana.mendes@iscte.pt
$^2$Department of Mathematics
IST - Technical University of Lisbon
Av. Rovisco Pais 1, 1049-001 Lisbon, PORTUGAL
e-mail: sramos@math.ist.utl.pt


Abstract.The main purpose of this paper is to present how to construct a kneading theory for some particular classes of two-dimensional triangular maps. This is done by defining a tensor product between the polynomials and matrices corresponding to the one-dimensional basis map and fiber map. We also define a Markov partition by rectangles for the phase space of these maps. A direct consequence of these results is the computation of the topological entropy of two-dimensional triangular maps. The connection between kneading theory and subshifts of finite type is shown by using a commutative diagram derived from the homological configurations associated with $m-$modal maps of the interval.

Received: November 5, 2003

AMS Subject Classification: 37B10, 37B40, 37E30, 15A69

Key Words and Phrases: triangular maps, kneading theory, Markov partitions, topological entropy, tensor product

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 10
Issue: 4