Kneading Ambiguity

Kneading Theory for Triangular Maps

Abstract. 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 computati...

Combinatorics of the Kneading Map

On Rationality of Kneading Determinants

In this section, R denotes a ring with identity I. We study conditions under which I - Aλ and I - Bλ are left coprime or right coprime, where A, B ∈ R. As applications, we get sufficient conditions under which the Kneading determinant of a finite rank pair of operators on an infinite dimensional space is rational.

Three-dimensional Numerical Simulation of Dough Kneading

In this article we report on work concerned with the three-dimensional numerical simulation of dough mixing that arises in the food processing industry. Two dough mixers at various rotation speeds are studied, one with one stirrer and the other with two stirrers. Various types of fluid models are incorporated in this work. Numerical simulations are based on three dimensions in the cylindrical c...

Reducing Quadratic Forms by Kneading Sequences

We introduce an invertible operation on finite sequences of positive integers and call it “kneading”. Kneading preserves three invariants of sequences — the parity of the length, the sum of the entries, and one we call the “alternant”. We provide a bijection between the set of sequences with alternant a and parity s and the set of Zagier-reduced indefinite binary quadratic forms with discrimina...