Hyperbolicity properties of $C\sp 2$ multi-modal Collet-Eckmann maps without Schwarzian derivative assumptions
نویسندگان
چکیده
منابع مشابه
On Iterated Positive Schwarzian derivative Maps
The families of one-dimensional maps have been the object of many studies since [Sharkovsky, 1964], for instance in [Sharkovsky et al., 1997] or in [de Melo & van Strien, 1993], whose authors also studied this subject, we have two large surveys of the enormous effort made in the last decades in this field of work. We adopt the usual definitions as for instance symbolic dynamics or topological e...
متن کاملAnalyticity of the Srb Measure for Holomorphic Families of Quadratic-like Collet-eckmann Maps
We show that if ft is a holomorphic family of quadratic-like maps with all periodic orbits repelling so that for each real t the map ft is a real Collet-Eckmann S-unimodal map then, writing μt for the unique absolutely continuous invariant probability measure of ft, the map
متن کاملStatistical Properties of Unimodal Maps: Smooth Families with Negative Schwarzian Derivative
We prove that there is a residual set of families of smooth or analytic unimodal maps with quadratic critical point and negative Schwarzian derivative such that almost every non-regular parameter is Collet-Eckmann with subexponential recurrence of the critical orbit. Those conditions lead to a detailed and robust statistical description of the dynamics. This proves the Palis conjecture in this ...
متن کاملA Proof That S-unimodal Maps Are Collet-eckmann Maps in a Specific Range of Their Bifurcation Parameters
Generally, Collet-Eckmann maps require unimodality and multimodality. The inverse is not true. In this paper, we will prove that S-unimodal maps are Collet-Eckmann maps in a specific range of their bifurcation parameters. The proof is based on the fact that the family of robustly chaotic unimodal maps known in the literature are all topologically conjugate to one another and the fact that if tw...
متن کاملErgodic Properties of Sub-hyperbolic Functions with Polynomial Schwarzian Derivative
The ergodic theory and geometry of the Julia set of meromorphic functions on the complex plane with polynomial Schwarzian derivative is investigated under the condition that the forward trajectory of asymptotic values in the Julia set is bounded and the map f restricted to its closure is expanding, the property refered to as subexpanding. We first show the existence, uniqueness, conservativity ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1990
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1990-0994169-6