This is a one-stop introduction to the methods of ergodic theory applied to holomorphic
iteration. The authors begin with introductory chapters presenting the necessary tools from …

The average of a smooth function φ with respect to the SRB measure μ t of a smooth one-
parameter family ft of piecewise expanding interval maps is not always Lipschitz (Baladi …

We study the susceptibility function Ψ (z)= n= 0^ ∞ ∫ z^ n X (y)\rho_0 (y) ∂ ∂ y φ (f^ n (y))\,
dy associated to the perturbation f_t\,=\, f\,+\, tX\, ∘\, f of a piecewise expanding interval map …

The purpose of this paper is to initiate a theory concerning the dynamics of asymptotically
holomorphic polynomial-like maps. Our maps arise naturally as deep renormalizations of …

Solenoidal attractors with bounded combinatorics are shy Page 1 Annals of Mathematics 191
(2020), 1–79 https://doi.org/10.4007/annals.2020.191.1.1 Solenoidal attractors with bounded …

We describe a new and robust method to prove rigidity results in complex dynamics. The
new ingredient is the geometry of the critical puzzle pieces: under control of geometry and …

The field of one-dimensional dynamics, real and complex, emerged from obscurity in the
1970s and has been intensely explored ever since. It combines the depth and complexity of …

We consider a family of strongly-asymmetric unimodal maps {f_t\} _ t ∈ 0, 1 ft t∈ 0, 1 of the
form f_t= t ⋅ f ft= t· f where f: 0, 1 → 0, 1 f: 0, 1→ 0, 1 is unimodal, f (0)= f (1)= 0 f (0)= f (1)= 0, f …

The purpose of this paper is to initiate a theory concerning the dynamics of asymptotically
holomorphic polynomial-like maps. Our maps arise naturally as deep renormalizations of …

We study the dynamics of the renormalization operator acting on the space of pairs (v, t),
where v is a diffeomorphism and t belongs to [0, 1], interpreted as unimodal maps x--> v (q_t …