John Hamal Hubbard

431 Malott Hall
Department of Mathematics
Cornell University
Ithaca NY 14853

phone: (607) 255-6495

email: jhh8 at


Differential equations are the main way in which mathematical models of real systems are constructed, and understanding their behavior is the main contribution a mathematician can make to applications. I am interested in understanding the behavior of differential equations and their close relatives: iterative systems. In particular, I try to see how such systems behave in the complex domain, largely because complex analysis brings new and powerful techniques to bear on the problems.

The availability of powerful computers and computer graphics has changed the way this sort of research is done. In the course of investigations of even such simple iterative systems as quadratic polynomials, amazing pictures show up, rather as artifacts to be investigated than as man-made objects. I anticipate that this sort of experimental mathematics will become a major trend.

Most of my research over the last five years has been devoted to dynamics in several complex variables. I have co-authored four foundational papers in the field. I am also writing three books on a very advanced level, one giving a treatment of Teichmüller space and its applications in theorems of Bill Thurston, the second on dynamics of one complex variable, and the third on differential equations.


Vector Calculus, Linear Algebra, and Differential Forms, A Unified Approach (with Barbara Burke Hubbard).

Teichmüller Theory and Applications to Geometry, Topology, and Dynamics, Volume I: Teichmüller theory

Calcul Scientifique de la théorie à la pratique, Volume I: Equations algébriques, traitement du signal et géométrie effective (with Florence Hubert).

Calcul Scientifique de la théorie à la pratique, Volume II: Equations différentielles et équations aux dérivées partielles (with Florence Hubert).

Differential Equations: A dynamical systems approach (with Beverly West).

Selected Papers:

Multicorns are not path connected (with Dierk Schleicher).

An analytic construction of the Deligne-Mumford compactification of the moduli space of curves (with Sarah Koch).

A first look at differential algebra (with Benjamin Lundell).

Newton's method applied to two quadratic equations in C^2 viewed as a global dynamical system (with Peter Papadopol).

Exponential Thurston maps and limits of quadratic differentials (with Dierk Schleicher and Mitsuhiro Shishikura).

Equidistribution of horocyclic flows on complete hyperbolic surfaces of finite area (with Robyn Miller).

The KAM theorem

Andreev's theorem on hyperbolic polyhedra (with Roland Roeder and William Dunbar).

Parametrizing unstable and very unstable manifolds.

A proof of Kolmogorov's theorem (with Yulij Ilyashenko).

A geometric view of rational Landen transformations (with Victor Moll).

Farey curves (with Xavier Buff and Christian Henriksen).

How to find all roots of complex polynomials by Newton's method (with Dierk Schleicher and Scott Sutherland).

Linked solenoid mappings and the nontransversality locus invariant (with Ralph Oberste-Vorth).

The convergence of an Euler approximation of an initial value problem is not always obvious (with Beverly West and Samer Habre).

A compactification of Hénon mappings in $\C^2$ as dynamical systems (with Peter Papadopol and Vladimir Veselov).

Preface to the book The Mandelbrot Set, theme and variations .

A Fatou-Bieberbach domain avoiding a neighborhood of a variety of codimension 2 (with Greg Buzzard).

Hairs for the complex exponential family (with Clara Bodelón, Bob Devaney, Michael Hayes, and Gareth Roberts).

The forced damped pendulum: chaos, complication and control.

Groups of automorphisms of tree and their limit sets (with Sa'ar Hersonsky).

Hénon mappings in the complex domain II: projective and inductive limits of polynomials (with Ralph Oberste-Vorth).

The spider algorithm (with Dierk Schleicher).

Hénon mappings in the complex domain I: the global topology of dynamical space (with Ralph Oberste-Vorth).

Superattractive Fixed Points in $\C^n$ (with Peter Papadopol)

A proof of Thurston's topological characterization of rational functions (with Adrien Douady).

Local Connectivity of Julia sets and bifurcation loci: three theorems of J-C Yoccoz.

The iteration of cubic polynomials part II: patterns and parapatterns (with Bodil Branner).

The classification of critically preperiodic polynomials as dynamical systems (with Benjamin Bielefeld and Yuval Fisher).

The classification of topologically expansive Lorenz maps (with Colin Sparrow).

A proof of the uniformization theorem for arbitrary plane domains (with Benjamin Wittner and Yuval Fisher).

The iteration of cubic polynomials part I: the global topology of parameter space (with Bodil Branner).

The Hénon mapping in the complex domain.

On the dynamics of polynomial-like mappings (with Adrien Douady).

The Orsay Notes English, French (with Adrien Douady).

Itération des polynômes quadratiques complexes (with Adrien Douady).

The monodromy of projective structures.

On the convex hull genus of space curves.

The space of closed subgroups of $\R^2$ (with Ibrahim Pourezza).

Quadratic differentials and foliations (with Howie Masur).

On the existence and uniqueness of Strebel differentials (with Howie Masur).

On the density of Strebel differentials (with Adrien Douady).


Le theorem de M. Artin sur les solutions d'equations analytiques.

On the cohomology of Nash sheaves.

A note on nonrigid Nash structures.

Sur les sections analytiques de la courbe universelle de Teichmüller (my thesis).

Selected Talks:

Marden Lecture, Forced Damped Pendulum, March 2008

A talk for the Undergraduate Math Club at Cornell, explaining the Mandelbrot Set, April 2008

In memory of Adrien Douady, Paris, May 2008

The Bott-Duffin synthesis: in memory of Raoul Bott, Montreal, June 2008

Monodromy and Henon maps, Oberwolfach, October 2008

Transversality according to Adam Epstein, Oberwolfach, October 2008

Monomial mappings and Hilbert modular varieties, October 2008

Some new approaches to Henon mappings, Stony Brook, June 2009

Parabolic Blow ups, Banff, February 21, 2011

The Price of Anarchy, Public Lecture, Cornell University, April 2011


Cornell math department

Centre de Mathématiques et Informatique

Oliver Club

Dynamics seminar

Dynamics page at Cornell

Matrix Editions

The PhD thesis of C. Lipa.