This paper contains some sufficient condition for the point zero to be a global attractor for nonlinear recurrence of second order.
@article{bwmeta1.element.bwnjournal-article-div17i1-2n6bwm, author = {Dobies\l aw A. Bobrowski}, title = {Global attractor for nonlinear recurrence of second order}, journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization}, volume = {17}, year = {1997}, pages = {83-88}, zbl = {0907.39013}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-div17i1-2n6bwm} }
Dobiesław A. Bobrowski. Global attractor for nonlinear recurrence of second order. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 17 (1997) pp. 83-88. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-div17i1-2n6bwm/
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