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Rigidity for real polynomials
We prove the topological (or combinatorial) rigidity property for real polynomials with all critical points real and nondegenerate, which completes the last step in solving the density of Axiom AExpand
On stochastic stability of non-uniformly expanding interval maps
We study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under mild conditions, we prove strong stochastic stability.Expand
Hausdorff dimension of the graphs of the classical Weierstrass functions
We show that the graph of the classical Weierstrass function $$\sum _{n=0}^\infty \lambda ^n \cos (2\pi b^n x)$$∑n=0∞λncos(2πbnx) has Hausdorff dimension $$2+\log \lambda /\log b$$2+logλ/logb, forExpand
Density of hyperbolicity in dimension one
Here we say that a real polynomial is hyperbolic or Axiom A, if the real line is the union of a repelling hyperbolic set, the basin of hyperbolic attracting periodic points and the basin of infinity.Expand
Combinatorial rigidity for unicritical polynomials
We prove that any unicritical polynomial fc : z zd + c which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. This implies that the connectednessExpand
Large derivatives, backward contraction and invariant densities for interval maps
In this paper, we study the dynamics of a smooth multimodal interval map f with non-flat critical points and all periodic points hyperbolic repelling. Assuming that |Dfn(f(c))|→∞ as n→∞ holds for allExpand
Summability implies Collet–Eckmann almost surely
  • Bing Gao, W. Shen
  • Mathematics
  • Ergodic Theory and Dynamical Systems
  • 16 November 2011
Abstract We provide a strengthened version of the famous Jakobson's theorem. Consider an interval map $f$ satisfying a summability condition. For a generic one-parameter family ${f}_{t} $ of mapsExpand
Statistical properties of one-dimensional maps under weak hyperbolicity assumptions
For a real or complex one-dimensional map satisfying a weak hyperbolicity assumption, we study the existence and statistical properties of physical measures, with respect to geometric referenceExpand
Invariant Measures Exist Without a Growth Condition
Given a non-flat S-unimodal interval map f, we show that there exists C which only depends on the order of the critical point c such that if |Dfn(f(c))|≥C for all n sufficiently large, then f admitsExpand
On the metric properties of multimodal interval maps and C2 density of Axiom A
In this paper, we shall prove that Axiom A maps are dense in the space of C2 interval maps (endowed with the C2 topology). As a step of the proof, we shall prove real and complex a priori bounds forExpand