We discuss a generalization of the ∗-product in kneading theory to maps with an arbitrary finite number of turning points. This is based on an investigation of the factorization of permutations into products of permutations with some special properties relevant for dynamics on the unit interval.

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

A complete description of the iterated monodromy groups of postcritically finite backward polynomial iterations is given in terms of their actions on rooted trees and automata generating them. We describe an iterative algorithm for finding kneading automata associated with post-critically finite topological polynomials and discuss some open questions about iterated monodromy groups of polynomials.

We describe the iterated monodromy groups associated with post-critically finite quadratic polynomials, and explicit their connection to the ‘kneading sequence’ of the polynomial. We then give recursive presentations by generators and relations for these groups, and study some of their properties, like torsion and ‘branchness’.

Abstract: Solid dispersion (SD) is one of the oldest and widely utilized techniques to improve solubility slowly dissolving drugs. A variety pharmaceutically compatible additives using different emerging technology used for preparing SDs. Multiple approaches were designed prepare SDs by such as kneading, co-milling, fusion, solvent evaporation various solvent-associated methods. The selection a...

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In this note we fill in some essential details which were missing from our paper. In the case of an escape region Eh with non-trivial kneading sequence, we prove that the canonical parameter t can be expressed as a holomorphic function of the local parameter η = a−1/μ (where a is the periodic critical point). Furthermore, we prove that for any escape region Eh of grid period n ≥ 2, the winding ...

We describe the iterated monodromy groups associated with post-critically finite quadratic polynomials, and make explicit their connection to the 'kneading sequence' of the polynomial. We then give recursive presentations by generators and relations for these groups, and study some of their properties, like torsion and 'branchness'.