In 1967, the first author wrote 'Research Problems in Function Theory', which was published
by the Athlone Press of the University of London. There had been earlier problem collections …

Rigidity is a fundamental phenomenon in hyperbolic geometry and holomorphic dynamics.
Its meaning is that the metric properties of certain manifolds or dynamical systems are …

We prove the Feigenbaum-Coullet-Tresser conjecture on the hyperbolicity of the
renormalization transformation of bounded type. This gives the first computer-free proof of …

Generic Hyperbolicity in the Logistic Family Page 1 Annals of Mathematics, 146 (1997), 1-52
Generic hyperbolicity in the logistic family By JACEK GRACZYK* and GRZEGORZ SWIATEK …

In this paper we complete a program to study measurable dynamics in the real quadratic
family. Our goal was to prove that almost any real quadratic map, c∈[-2, 1/4], has either an …

In this paper we prove that in any non-trivial real analytic family of quasiquadratic maps,
almost any map is either regular (ie, it has an attracting cycle) or stochastic (ie, it has an …

Robust chaos is defined by the absence of periodic windows and coexisting attractors in
some neighborhoods in the parameter space of a dynamical system. This unique book …

We give new proofs that the Mandelbrot set is locally connected at every Misiurewicz point
and at every point on the boundary of a hyperbolic component. The idea is to show …

Rigidity for Real Polynomials Page 1 Annals of Mathematics, 165 (2007), 749-841 Rigidity for
real polynomials By O. Kozlovski, W. Shen, and S. van Strien* Abstract We prove the …

Density of Hyperbolicity in Dimension One Page 1 Annals of Mathematics, 166 (2007), 145-182
Density of hyperbolicity in dimension one By O. Kozlovski, W. Shen, and S. van Strien 1 …