We study geometric and statistical properties of complex rational maps satisfying a non-
uniform hyperbolicity condition called “Topological Collet–Eckmann”. This condition is …

We study the thermodynamic formalism of a complex rational map f of degree at least two,
viewed as a dynamical system acting on the Riemann sphere. More precisely, for a real …

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| Df n (f (c))|→∞ as …

Let f. z/D pz/= qz/be a rational map with p and q relatively prime polynomials. The degree d
D deg. f/of f is defined to be the maximum of the degrees of p and q. In the following we will …

There is a wealth of results in the literature on the thermodynamic formalism for potentials
that are, in some sense,“hyperbolic”. We show that for a sufficiently regular one-dimensional …

The escape rates thru a ball in a dynamical system have been much studied. Understanding
the asymptotic behavior of the escape rate as the radius of the ball tends to zero is an …

Using quasiconformal surgery, we prove that any primitive, postcritically-finite hyperbolic
polynomial can be tuned with an arbitrary generalized polynomial with non-esca** critical …

It is well known that the Manneville–Pomeau map with a parabolic fixed point of the form is
stochastically stable for α≥ 1 and the limiting measure is the Dirac measure at the fixed …

In holomorphic dynamics, complex box map**s arise as first return maps to well-chosen
domains. They are a generalization of polynomial-like map**, where the domain of the …

On stochastic stability of non-uniformly expanding interval maps Page 1 Proc. London Math.
Soc. (3) 107 (2013) 1091–1134 Cо2013 London Mathematical Society doi:10.1112/plms/pdt013 …