Geodesic
Poincar\'e's theorem and its applications to the~convergence of continued fractions
Sbornik. Mathematics, Tome 189 (1998) no. 12, pp. 1749-1764

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

A refined version of a classical theorem of Poincaré on difference equations with coefficients having limits is established. Applications include several results that are similar to well-known theorems of Van Vleck, Thron–Waadeland, and Perron, but are proved under considerably weaker assumptions. 
@article{SM_1998_189_12_a1,
     author = {V. I. Buslaev},
     title = {Poincar\'e's theorem and its applications  to the~convergence of continued fractions},
     journal = {Sbornik. Mathematics},
     pages = {1749--1764},
     publisher = {mathdoc},
     volume = {189},
     number = {12},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_12_a1/}
}
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V. I. Buslaev. Poincar\'e's theorem and its applications  to the~convergence of continued fractions. Sbornik. Mathematics, Tome 189 (1998) no. 12, pp. 1749-1764. http://geodesic.mathdoc.fr/item/SM_1998_189_12_a1/