IMS Thesis Server

This is the Server of Theses in Dynamical Systems hosted by the IMS at Stony Brook.

1986
On the Bifurcation Loci of Rational Maps of Degree Two
Ben Wittner   ( Cornell University, USA )
Advisor: John Hubbard

1992
Sur Quelques Problèmes de Dynamique Holomorphe
Thierry Bousch   ( Université d'Orsay, FRANCE )
Advisor: Adrien Douady

1993
Topological Conditions for Positive Lyapunov Exponent in Unimodal Maps
Duncan Sands   ( Cambridge University, UK )
Advisor: Colin Sparrow

1994
Cylinders for Iterated Rational Maps
Kevin M. Pilgrim   ( University of California, Berkeley, USA )
Advisor: Curtis T. McMullen

1994
Internal Addresses in the Mandelbrot Set and Irreducibility of Polynomials
Dierk Schleicher   ( Cornell University, USA )
Advisor: John H. Hubbard

1995
Rotation Sets and Entropy
Jaroslaw Kwapisz   ( SUNY at Stony Brook, USA )
Advisor: John Milnor

1995
Conformal Measures in Polynomial Dynamics
Eduardo Prado   ( Stony Brook University, USA )
Advisor: Mikhail Lyubich

1995
Local Connectivity and Lebesgue Measure of Polynomial Julia Sets
Brian Yarrington   ( Stony Brook University, USA )
Advisor: Mikhail Lyubich

1996
Periodic Points in S-Integer Dynamical Systems
Vijay Chothi   ( University of East Anglia, UK )
Advisor: Thomas Ward and Graham Everest

1996
Scaling Laws for Quadratic Maps
LeRoy Wenstrom   ( Stony Brook University, USA )
Advisor: Mikhail Lyubich

1997
Dynamical Studies in Several Complex Variables
Mattias Jonsson   ( The Royal Institute of Technology, Stockholm, SWEDEN )
Advisor: Michael Benedicks

1997
Rational Rays and Critical Portraits of Complex Polynomials
Jan Kiwi   ( SUNY at Stony Brook, USA. )
Advisor: John Milnor

1997
Renormalization for Siegel Discs
Andrew D. Burbanks   ( Loughborough University, UK )
Advisor: Andrew Osbaldestin

1997
Complex bounds for renormalization of one-dimensional dynamical systems
Mikhail Yampolsky   ( Stony Brook University, USA )
Advisor: Mikhail Lyubich

1998
Dynamical Constraints on Group Actions
Gary Morris   ( University of East Anglia, UK )
Advisor: Thomas Ward

1998
Les Attracteurs des Systèmes Dynamiques Dissipatifs de Lorenz et de Liénard : Nombre, Forme et Localisation
Sébastien Neukirch   ( Université Paris VI, FRANCE )
Advisor: Hector Giacomini

1998
On the Combinatorics of External Rays in the Dynamics of the Complex Henon Map
Ricardo A. Oliv   ( Cornell University, USA )
Advisor: John Smillie

1998
Parbolic Limits of Renormalization
Benjamin Hinkle   ( Stony Brook University, USA )
Advisor: Mikhail Lyubich

1999
The Parabolic Implosion for $f_0(z) = z + z^{\nu+1} + \mathcal{O}(z^{\nu+2})$
Richard Oudkerk   ( University of Warwick, UK )
Advisor: Tan Lei

1999
Rational Parameter Rays of Multibrot Sets
Dominik Eberlein (Diploma Thesis)   ( Technische Universität, München, GERMANY )
Advisor: Dierk Schleicher

2000
Arithmetic Dynamical Systems
Richard Craig Miles   ( University of East Anglia, UK )
Advisor: Thomas Ward

2000
Dynamique des Fonctions Rationelles sur des Corps Locaux
Juan Rivera Letelier   ( Université Paris Sud (Orsay), FRANCE )
Advisor: J. C. Yoccoz

2000
Arithmetic of Numbers of Periodic Points
Yash Paul Puri   ( University of West Anglia, UK )
Advisor: Thomas Ward

2001
Recherche d'Ensembles de Julia de Mesure de Lebesgue Strictement Positive.
Arnaud Cheritat   ( Université Paris Sud (Orsay), FRANCE )
Advisor: Adrien Douady

2001
Using Spider Theory to Explore Parameter Spaces
David A. Brown   ( Cornell University, USA )
Advisor: John Hubbard

2001
Arcs in Multibrot Sets, Locally Connected Julia Sets and Their Construction by Quasiconformal Surgery
Johannes Riedl   ( Technische Universität, München, GERMANY )
Advisor: Dierk Schleicher

2001
Nombre de rotation et dynamique faiblement hyperbolique
Sylvain Crovisier   ( Université Paris Sud (Orsay), FRANCE )
Advisor: Jean-Christophe Yoccoz

2002
Dynamics of Quadratic Polynomials: Geometry and Combinatorics of the Principal Nest
Rodrigo A. Pérez   ( SUNY at Stony Brook, USA )
Advisor: Mikhail Lyubich and John Milnor

2002
On the Numerical Construction of Hyperbolic Structures for Complex Dynamical Systems
Suzanne Lynch Hruska   ( Cornell University, USA )
Advisor: John Smillie

2002
Homeomorphisms on Edges of the Mandelbrot Set
Wolf Jung   ( Rheinisch-Westfälische Technische Hochschule, Aachen, GERMANY )
Advisor: Volker Enss

2003
Dynamics of Exponential Maps
Lasse Rempe   ( Christian-Albrechts Universität, Kiel, GERMANY )
Advisor: Walter Bergweiler

2003
Semiconjugacies in Complex Dynamics with Parabolic Cycles
Tomoki Kawahira   ( University of Tokyo, JAPAN )
Advisor: Takashi Tsuboi

2003
Parameter Rays for the Exponential Family
Markus Förster (Diploma Thesis)   ( Technische Universität, München, GERMANY )
Advisor: Dierk Schleicher

2003
A Rigorous Numerical Method in Infinite Dimensions
Sarah Day   ( Georgia Institute of Technology, USA )
Advisor: Konstantin Mischaikow

2003
The Arithmetic of Realizable Sequences
Patrick Moss   ( University of East Anglia, UK )
Advisor: Thomas Ward and Graham Everest

2004
Orbit Counting Far From Hyperbolicity
Victoria Stangoe   ( University of East Anglia, UK )
Advisor: Thomas Ward and Graham Everest

2004
The Collet-Eckmann Condition for Rational Functions on the Riemann Sphere
Magnus Aspenberg   ( The Royal Institute of Technology, Stockholm, SWEDEN )
Advisor: Michael Benedicks

2004
Self-similarity of the Madelbrot Set and parabolic Bifurcation
Rogelio Valdez   ( Stony Brook University, USA )
Advisor: Mikhail Lyubich

2005
Generic Properties of Lagrangian Systems and Conservative Diffeomorphisms
Radu Saghin   ( Northwestern University, USA )
Advisor: Zhihong Jeff Xia

2005
Topology for the Basins of Attraction of Newton's Method in Two Complex Variables
Roland K. W. Roeder   ( Cornell University, USA )
Advisor: John H. Hubbard

2005
Towards Classification of Laminations Associated to Quadratic Polynomials
Carlos Cabrera   ( SUNY at Stony Brook, USA )
Advisor: Mikhail Lyubich

2005
The Connected Isentropies Conjecture in a Space of Quartic Polynomials
Anca Ruxandra Radulescu   ( SUNY at Stony Brook, USA )
Advisor: John Milnor

2005
Some remarks on Local Connectivity at the Feigenbaum Point
Gregory Janks   ( Stony Brook University, USA )
Advisor: Mikhail Lyubich

2006
Newton's Method as a Dynamical System
Johannes Rueckert   ( International University Bremen, GERMANY )
Advisor: Dierk Schleicher

2006
Studies in Topological Dynamics with Emphasis on Cellular Automata
T.K. Subrahmonian Moothathu   ( University of Hyderabad, INDIA )
Advisor: V. Kannan

2006
Hubbard Trees and Kneading Sequences for Unicritical and Cubic Polynomials
Alexandra Kaffl   ( International University Bremen, GERMANY )
Advisor: Dierk Schleicher

2007
Dynamics of Certain Transcendental Entire and Meromorphic Functions
Tarakanta Nayak   ( Indian Institute of Technology Guwahati, INDIA )
Advisor: M. Guru Prem Prasad

2007
A monotonicity conjecture for the entropy of Hubbard trees
Tao Li   ( Stony Brook University, USA )
Advisor: John Milnor

2008
Renormalization and Non-Rigidity
Vasu Venkata Mohana Sarma Chandramouli   ( Stony Brook University, USA )
Advisor: Marco Martens

2008
Henon-like Maps and Renormalisation
Peter Hazard   ( Stony Brook University, USA )
Advisor: Marco Martens

2009
Dynamics of complex unicritical polynomials
Davoud Cheraghi   ( Stony Brook University, USA )
Advisor: Mikhail M. Lyubich

2010
Non-recurrent dynamics in the exponential family
Anna Benini   ( Stony Brook University, USA )
Advisor: Mikhail M. Lyubich

2011
Dynamics of McMullen maps and Thurston-type theorem
Xiaoguang Wang   ( Fudan University, CHINA and Université )
Advisor: Weiyuan Qiu (Fudan) and Tan Lei (Angers)

2011
A classification of postcritically finite Newton maps
Yauhen Mikulich   ( Jacobs University )
Advisor: Dierk Schleicher

2011
Renormalization of Three Dimensional Henon Map
Young Woo Nam   ( Stony Brook University, USA )
Advisor: Marco Martens

2012
Boundary Values of the Thurston Pullback Map
Russell Lodge   ( Indiana University )
Advisor: Kevin Pilgrim

2015
On the route to chaos for two-dimensional modestly area-contracting analytic maps
Ying Chi   ( Stony Brook University, USA )
Advisor: Marco Martens

2016
Infinitely primitively renormalizable polynominals of bounded type
Joseph Adams   ( Stony Brook University, USA )
Advisor: Mikhail Lyubich


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