On étend le théorème d'hyperbolicité de Mañé pour traiter des orbites qui passent par des voisinages critiques pour des applications multimodales de l'intervalle. On démontre que, pour des cocycles bien adaptés, ces applications sont dilatantes.
We give a cocycle expansivity result for multimodal interval maps with non-flat critical points. It extends the Mañé hyperbolicity theorem to also describe orbits which pass near critical points.
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@article{CRMATH_2007__345_1_39_0, author = {Dobbs, Neil}, title = {Expanding cocycles for interval maps}, journal = {Comptes Rendus. Math\'ematique}, pages = {39--44}, publisher = {Elsevier}, volume = {345}, number = {1}, year = {2007}, doi = {10.1016/j.crma.2007.06.002}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.06.002/} }
TY - JOUR AU - Dobbs, Neil TI - Expanding cocycles for interval maps JO - Comptes Rendus. Mathématique PY - 2007 SP - 39 EP - 44 VL - 345 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.06.002/ DO - 10.1016/j.crma.2007.06.002 LA - en ID - CRMATH_2007__345_1_39_0 ER -
Dobbs, Neil. Expanding cocycles for interval maps. Comptes Rendus. Mathématique, Tome 345 (2007) no. 1, pp. 39-44. doi : 10.1016/j.crma.2007.06.002. http://archive.numdam.org/articles/10.1016/j.crma.2007.06.002/
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