Geodesic
On the index of invariant domains of homeomorphisms of
Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 207-221

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The index is estimated for invariant domains preserving the orientation of homeomorphisms of two-dimensional manifolds. Figures: 4. Bibliography: 5 titles. 
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V. S. Medvedev. On the index of invariant domains of homeomorphisms of. Sbornik. Mathematics, Tome 62 (1989) no. 1, pp. 207-221. http://geodesic.mathdoc.fr/item/SM_1989_62_1_a13/