We consider families of hyperbolic maps and describe conditions for a fixed reference point to have its orbit evenly distributed for maps corresponding to generic parameter values.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm206-0-15, author = {Mark Pollicott}, title = {Normal points for generic hyperbolic maps}, journal = {Fundamenta Mathematicae}, volume = {205}, year = {2009}, pages = {271-280}, zbl = {1186.37040}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm206-0-15} }
Mark Pollicott. Normal points for generic hyperbolic maps. Fundamenta Mathematicae, Tome 205 (2009) pp. 271-280. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm206-0-15/