Kneading Theory for Triangular Maps

Details Kneading Theory for Triangular Maps Kneading Theory for Triangular Maps

2003-01-07

arxiv.org/abs/math/0301054v2

Mathematics

Dynamical Systems

22 pages,6 figures

Scientific paper

The main purpose of this paper is to present a kneading theory for 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 rigorous 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 to $m-$modal maps of the interval.

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