Classification of continuously transitive circle groups

AUTOMORPHISM GROUPS OF SOME NON-TRANSITIVE GRAPHS

An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for ij, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. Balaban introduced some monster graphs and then Randic computed complexit...

Transitive Circle Exchange Maps with Flips

Circle exchange transformations (CETs) and interval exchange transformations (IETs) form a fundamental class of objects studied in measurable dynamics, noted for their simple definition yet rich variety of behaviours (see [16]). They arise naturally in the study of polygonal billiards (see [1]), measured foliations (see [2, 9]) and flat surfaces (see [17, 18]). Moreover, transitive CETs arise i...

Groups of Circle Diffeomorphisms

On Transitive Permutation Groups

We assign names and new generators to the transitive groups of degree up to 15, reflecting their structure.

Two-transitive Lie groups

Using a characterization of parabolics in reductive Lie groups due to Furstenberg, elementary properties of buildings, and some algebraic topology, we give a new proof of Tits’ classification of 2-transitive Lie groups. Among many other results, Tits classified in [41] all 2-transitive Lie groups. His proof is based on Dynkin’s classification of maximal complex subalgebras in complex simple Lie...