scholarly journals Kneading theory

Scholarpedia ◽  
2010 ◽  
Vol 5 (11) ◽  
pp. 3956
Author(s):  
Toby Hall
Keyword(s):  
2004 ◽  
Vol 2004 (38) ◽  
pp. 2019-2038 ◽  
Author(s):  
J. Leonel Rocha ◽  
J. Sousa Ramos

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.


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

2003 ◽  
Vol 13 (07) ◽  
pp. 1701-1709 ◽  
Author(s):  
Nuno Martins ◽  
Ricardo Severino ◽  
J. Sousa Ramos

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.


1995 ◽  
Vol 05 (05) ◽  
pp. 1339-1349 ◽  
Author(s):  
H. BRUIN

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.


Nonlinearity ◽  
1993 ◽  
Vol 6 (3) ◽  
pp. 349-367 ◽  
Author(s):  
P Glendinning

2003 ◽  
Vol 13 (01) ◽  
pp. 115-122 ◽  
Author(s):  
JUNG-CHAO BAN ◽  
CHENG-HSIUNG HSU ◽  
SONG-SUN LIN

This study demonstrates the devil's staircase structure of topological entropy functions for one-dimensional symmetric unimodal maps with a gap inside. The results are obtained by using kneading theory and are helpful in investigating the communication of chaos.


2009 ◽  
Vol 42 (3) ◽  
pp. 1529-1538 ◽  
Author(s):  
Acilina Caneco ◽  
Clara Grácio ◽  
J. Leonel Rocha

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

2004 ◽  
Vol 24 (4) ◽  
pp. 957-985 ◽  
Author(s):  
J. F. ALVES ◽  
J. SOUSA RAMOS
Keyword(s):  

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