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Rigidity for real polynomials

- O. Kozlovski, W. Shen, S. V. Strien
- Mathematics
- 1 May 2007

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 A… Expand

On stochastic stability of non-uniformly expanding interval maps

- W. Shen
- Mathematics
- 13 July 2011

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

- W. Shen
- Mathematics
- 15 May 2015

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, for… Expand

Density of hyperbolicity in dimension one

- O. Kozlovski, W. Shen, S. V. Strien
- Mathematics
- 1 July 2007

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

- A. Avila, Jeremy A. Kahn, M. Lyubich, W. Shen
- Mathematics
- 12 July 2005

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 connectedness… Expand

Large derivatives, backward contraction and invariant densities for interval maps

- H. Bruin, J. Rivera-Letelier, W. Shen, Sebastian van Strien
- Mathematics
- 23 January 2008

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 all… Expand

Summability implies Collet–Eckmann almost surely

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 maps… Expand

Statistical properties of one-dimensional maps under weak hyperbolicity assumptions

- J. Rivera-Letelier, W. Shen
- Mathematics
- 1 April 2010

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 reference… Expand

Invariant Measures Exist Without a Growth Condition

- H. Bruin, W. Shen, S. V. Strien
- Mathematics
- 12 September 2003

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 admits… Expand

On the metric properties of multimodal interval maps and C2 density of Axiom A

- W. Shen
- Mathematics
- 1 May 2004

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 for… Expand

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