Kneading Theory: A Functorial Approach

1999 ◽  
Vol 204 (1) ◽  
pp. 89-114 ◽  
Author(s):  
J. F. Alves ◽  
J. Sousa Ramos
Keyword(s):  
Kneading Theory ◽  
Functorial Approach

scholarly journals The twofold way of super holonomy

2016 ◽  
Vol 28 (6) ◽  
Author(s):  
Josua Groeger
Keyword(s):  
Comparison Theorem ◽  
Wilson Loops ◽  
Holonomy Algebra ◽  
Functorial Approach

AbstractThere are two different notions of holonomy in supergeometry, the supergroup introduced by Galaev and our functorial approach motivated by super Wilson loops. Either theory comes with its own version of invariance of vectors and subspaces under holonomy. By our first main result, the Twofold Theorem, these definitions are equivalent. Our proof is based on the Comparison Theorem, our second main result, which characterises Galaev’s holonomy algebra as an algebra of coefficients, building on previous results. As an application, we generalise some of Galaev’s results to

scholarly journals Weighted kneading theory of one-dimensional maps with a hole

2004 ◽  
Vol 2004 (38) ◽  
pp. 2019-2038 ◽  
Author(s):  
J. Leonel Rocha ◽  
J. Sousa Ramos
Keyword(s):  
Hausdorff Dimension ◽  
Power Series ◽  
Formal Power Series ◽  
Topological Entropy ◽  
Escape Rate ◽  
One Dimensional ◽  
One Dimensional Maps ◽  
Formal Power ◽  
Kneading Theory

The purpose of this paper is to present a weighted kneading theory for one-dimensional maps with a hole. We consider extensions of the kneading theory of Milnor and Thurston to expanding discontinuous maps with a hole and introduce weights in the formal power series. This method allows us to derive techniques to compute explicitly the topological entropy, the Hausdorff dimension, and the escape rate.

Kneading theory and rotation intervals for a class of circle maps of degree one

Nonlinearity ◽  
1990 ◽  
Vol 3 (2) ◽  
pp. 413-452 ◽  
Author(s):  
L Alseda ◽  
F Manosas
Keyword(s):  
Circle Maps ◽  
Kneading Theory

Isentropic Real Cubic Maps

2003 ◽  
Vol 13 (07) ◽  
pp. 1701-1709 ◽  
Author(s):  
Nuno Martins ◽  
Ricardo Severino ◽  
J. Sousa Ramos
Keyword(s):  
Topological Entropy ◽  
Level Set ◽  
Topological Invariant ◽  
Symbolic Order ◽  
Kneading Theory ◽  
Theory Framework

Given a family of bimodal maps on the interval, we need to consider a second topological invariant, other than the usual topological entropy, in order to classify it. With this work, we want to understand how to use this second invariant to distinguish bimodal maps with the same topological entropy and, in particular, how this second invariant changes within a given type of topological entropy level set. In order to do that, we use the kneading theory framework and introduce a symbolic product * between kneading invariants of maps from the same topological entropy level set, for which we show that the second invariant is preserved. Finally, we also show that the change of the second invariant follows closely the symbolic order between bimodal kneading sequences.

scholarly journals A FUNCTORIAL APPROACH TO THE C*-ALGEBRAS OF A GRAPH

2002 ◽  
Vol 13 (03) ◽  
pp. 245-277 ◽  
Author(s):  
JACK SPIELBERG
Keyword(s):  
Structural Properties ◽  
Inductive Limit ◽  
Directed Graphs ◽  
Graph Algebras ◽  
C Algebras ◽  
Injective Homomorphisms ◽  
Functorial Approach

A functor from the category of directed trees with inclusions to the category of commutative C*-algebras with injective *-homomorphisms is constructed. This is used to define a functor from the category of directed graphs with inclusions to the category of C*-algebras with injective *-homomorphisms. The resulting C*-algebras are identified as Toeplitz graph algebras. Graph algebras are proved to have inductive limit decompositions over any family of subgraphs with union equal to the whole graph. The construction is used to prove various structural properties of graph algebras.

A functorial approach to near-rings

1979 ◽  
Vol 34 (1-2) ◽  
pp. 47-57 ◽  
Author(s):  
S. Feigelstock ◽  
A. Klein
Keyword(s):  
Functorial Approach

COMBINATORICS OF THE KNEADING MAP

1995 ◽  
Vol 05 (05) ◽  
pp. 1339-1349 ◽  
Author(s):  
H. BRUIN
Keyword(s):  
Topological Structure ◽  
Limit Set ◽  
Geometric Properties ◽  
Unimodal Maps ◽  
Omega Limit Set ◽  
Kneading Theory

The kneading map and the Hofbauer tower are tools, developed by F. Hofbauer and G. Keller, to study unimodal maps and the kneading theory. In this paper we survey the geometric properties of these tools. Results concerning the topological structure of the critical omega-limit set are obtained.

The anharmonic route to chaos: kneading theory

Nonlinearity ◽  
1993 ◽  
Vol 6 (3) ◽  
pp. 349-367 ◽  
Author(s):  
P Glendinning
Keyword(s):  
Route To Chaos ◽  
Kneading Theory
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