Geodesic
Representation of spaciously situated perfect attractors of diffeomorphisms by geodesic laminations
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 20 (2018) no. 2, pp. 159-174

Voir la notice de l'article provenant de la source Math-Net.Ru

The present paper is devoted to the topological classification of one-dimensional basiс sets of diffeomorphisms satisfying Smale's axiom A and defined on orientable surfaces of negative Euler characteristic equipped with a metric of constant negative curvature. Using methods of Lobachevsky geometry, each perfect one-dimensional attractor of A-diffeomorphism is uniquely associated with a geodesic lamination on the surface. It is established that, in the absence of special pairs of boundary periodic points in the attractor, there exists a homeomorphism of the surface homotopic to the identity that maps unstable manifolds of the basic set points into leaves of the geodesic lamination. Moreover, from the method of constructing geodesic laminations it follows that if the diffeomorphisms whose non-wandering sets contain perfect spaciously situated attractors are homotopic, then the geodesic laminations corresponding to these attractors coincide.
Keywords: diffeomorphism, perfect basiс set, attractor, repeller, geodesic lamination.
Mots-clés : axiom $A$ 
@article{SVMO_2018_20_2_a2,
     author = {V. Z. Grines and E. D. Kurenkov},
     title = {Representation of spaciously  situated perfect attractors of diffeomorphisms by  geodesic  laminations},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {159--174},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2018_20_2_a2/}
}
TY  - JOUR
AU  - V. Z. Grines
AU  - E. D. Kurenkov
TI  - Representation of spaciously  situated perfect attractors of diffeomorphisms by  geodesic  laminations
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2018
SP  - 159
EP  - 174
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2018_20_2_a2/
LA  - ru
ID  - SVMO_2018_20_2_a2
ER  - 
%0 Journal Article
%A V. Z. Grines
%A E. D. Kurenkov
%T Representation of spaciously  situated perfect attractors of diffeomorphisms by  geodesic  laminations
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2018
%P 159-174
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2018_20_2_a2/
%G ru
%F SVMO_2018_20_2_a2
V. Z. Grines; E. D. Kurenkov. Representation of spaciously  situated perfect attractors of diffeomorphisms by  geodesic  laminations. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 20 (2018) no. 2, pp. 159-174. http://geodesic.mathdoc.fr/item/SVMO_2018_20_2_a2/