Classifying C1+ structures on dynamical fractals: 2. Embedded trees

1995 ◽  
Vol 15 (5) ◽  
pp. 969-992 ◽  
Author(s):  
A. A. Pinto ◽  
D. A. Rand
Keyword(s):  
Moduli Spaces ◽  
Binary Tree ◽  
Conjugacy Classes ◽  
Expanding Maps ◽  
Bounded Geometry ◽  
Arbitrary Topology ◽  
Contact Points ◽  
Train Tracks ◽  
Smooth Conjugacy

AbstractWe classify the C1+α structures on embedded trees. This extends the results of Sullivan on embeddings of the binary tree to trees with arbitrary topology and to embeddings without bounded geometry and with contact points. We used these results in an earlier paper to describe the moduli spaces of smooth conjugacy classes of expanding maps and Markov maps on train tracks. In later papers we will use those results to do the same for pseudo-Anosov diffeomorphisms of surfaces. These results are also used in the classification of renormalisation limits of C1+α diffeomorphisms of the circle.

Classifying C1+ structures on dynamical fractals: 1. The moduli space of solenoid functions for Markov maps on train tracks

1995 ◽  
Vol 15 (4) ◽  
pp. 697-734 ◽  
Author(s):  
A. A. Pinto ◽  
D. A. Rand
Keyword(s):  
Moduli Space ◽  
Scaling Function ◽  
Matching Condition ◽  
Continuous Functions ◽  
Conjugacy Classes ◽  
Train Track ◽  
Hölder Continuous ◽  
Expanding Circle ◽  
Train Tracks ◽  
Smooth Conjugacy

AbstractSullivan's scaling function provides a complete description of the smooth conjugacy classes of cookie-cutters. However, for smooth conjugacy classes of Markov maps on a train track, such as expanding circle maps and train track mappings induced by pseudo-Anosov systems, the generalisation of the scaling function suffers from a deficiency. It is difficult to characterise the structure of the set of those scaling functions which correspond to smooth mappings. We introduce a new invariant for Markov maps called the solenoid function. We prove that for any prescribed topological structure, there is a one-to-one correspondence between smooth conjugacy classes of smooth Markov maps and pseudo-Hölder solenoid functions. This gives a characterisation of the moduli space for smooth conjugacy classes of smooth Markov maps. For smooth expanding maps of the circle with degree d this moduli space is the space of Hölder continuous functions on the space {0,…, d − 1}ℕ satisfying the matching condition.

scholarly journals A classification of spherical conjugacy classes

2016 ◽  
Vol 285 (1) ◽  
pp. 63-91
Author(s):  
Mauro Costantini
Keyword(s):  
Conjugacy Classes

Classification of Maximal Fuchsian Subsgroups of Some Bianchi Groups

1991 ◽  
Vol 34 (3) ◽  
pp. 417-422 ◽  
Author(s):  
L. Ya. Vulakh
Keyword(s):  
Quadratic Field ◽  
Complete Classification ◽  
Conjugacy Classes ◽  
Imaginary Quadratic Field ◽  
Ring Of Integers

AbstractLet d = 1,2, or p, prime p ≡ 3 (mod 4). Let Od be the ring of integers of an imaginary quadratic field A complete classification of conjugacy classes of maximal non-elementary Fuchsian subgroups of PSL(2, Od) in PGL(2, Od) is given.

Non-discrete Frieze Groups

2016 ◽  
Vol 59 (2) ◽  
pp. 234-243
Author(s):  
Alan F. Beardon
Keyword(s):  
Discrete Subgroup ◽  
Classical Case ◽  
Conjugacy Classes

AbstractThe classification of Euclidean frieze groups into seven conjugacy classes is well known, and many articles on recreational mathematics contain frieze patterns that illustrate these classes. However, it is only possible to draw these patterns because the subgroup of translations that leave the pattern invariant is (by definition) cyclic, and hence discrete. In this paper we classify the conjugacy classes of frieze groups that contain a non-discrete subgroup of translations, and clearly these groups cannot be represented pictorially in any practicalway. In addition, this discussion sheds light onwhy there are only seven conjugacy classes in the classical case.

Classification of finite groups according to the number of conjugacy classes

1985 ◽  
Vol 51 (4) ◽  
pp. 305-338 ◽  
Author(s):  
Antonio Vera López ◽  
Juan Vera López
Keyword(s):  
Finite Groups ◽  
Conjugacy Classes

Classification of real moduli spaces over genus 2 curves

1995 ◽  
Vol 57 (2) ◽  
pp. 207-215 ◽  
Author(s):  
Shuguang Wang
Keyword(s):  
Moduli Spaces ◽  
Genus 2 ◽  
Genus 2 Curves

scholarly journals A Recursive Binary Tree Method for Age Classification of Child Faces

2016 ◽  
Vol 8 (10) ◽  
pp. 56-66 ◽  
Author(s):  
Olufade F.W. Onifade ◽  
◽  
Joseph D. Akinyemi ◽  
Olashile S. Adebimpe
Keyword(s):  
Binary Tree ◽  
Tree Method

scholarly journals Complete Classification of Degree 7 for Genus 1

2021 ◽  
pp. 594-603
Author(s):  
Peshawa M. Khudhur
Keyword(s):  
Riemann Surface ◽  
Meromorphic Function ◽  
Symmetric Group ◽  
Compact Riemann Surface ◽  
Complete Classification ◽  
Conjugacy Classes ◽  
Branched Cover ◽  
Transitive Subgroup ◽  
Genus One

Assume that  is a meromorphic fuction of degree n where X is compact Riemann surface of genus g. The meromorphic function gives a branched cover of the compact Riemann surface X. Classes of such covers are in one to one correspondence with conjugacy classes of r-tuples (  of permutations in the symmetric group , in which  and s generate a transitive subgroup G of  This work is a contribution to the classification of all primitive groups of degree 7, where X is of genus one.

scholarly journals On classification of σ-conjugacy classes of a loop group

2016 ◽  
Vol 459 ◽  
pp. 29-42
Author(s):  
Sian Nie ◽  
Peipei Zhou
Keyword(s):  
Loop Group ◽  
Conjugacy Classes
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