Geodesic
Universal minimal flows of automorphism groups
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 28 (2003), p. 93 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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We investigate some connections between the Fra\'{\i}ss� theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures. We show, in particular, that results from the structural Ramsey theory can be quite useful in recognizing the universal minimal flows of this kind of groups. As result we compute universal minimal flows of several well known topological groups such as, for example, the automorphism group of the random graph, the automorphism group of the random triangle-free graph, the automorphism group of the $\infty$-dimensional vector space over a finite field, the automorphism group of the countable atomless Boolean algebra,etc. So we have here a reversal in the traditional relationship between topological dynamics and Ramsey theory, the Ramsey-theoretic results are used in proving theorems of topological dynamics rather than vice versa.
Classification : 05D10 05C55 22A10 22A05 22F05 37B05 37F20 54H20
Keywords: group actions, universal minimal flows, Fraisse theory, structural Ramsey theory 
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     author = {A. S. Kechris and V. Pestov and S. Todor\v{c}evi\'c},
     title = {Universal minimal flows of automorphism groups},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {93 },
     year = {2003},
     volume = {28},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASS_2003_28_a7/}
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A. S. Kechris; V. Pestov; S. Todorčević. Universal minimal flows of automorphism groups. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 28 (2003), p. 93 . http://geodesic.mathdoc.fr/item/BASS_2003_28_a7/