Office: Bromfield-Pearson Building, Room 214
Phone: (617) 627-3843

Research Interests

Dynamical systems, especially in dimensions 1 and 2; braids; combinatorial/geometric group theory; graphs; cellular automata.

For short vita, click here: Short Vita (5 pages)
For full vita, click here: Full Vita (14 pages)

Selected publications, 1970-2000:

On semi-stability for diffeomorphisms

Inventiones math. 14 (1970) 83-122

Differentiable Dynamics: an Introduction to the Orbit Structure of Diffeomorphisms

(The MIT Press: Cambridge, Mass., 1971) 297 pp.;

translations:

Izdat Mir, Moscow,1975

Dept. of Math., Beijing Univ. 1979

Filtrations, decompositions and explosions (with M. Shub)

Amer. J. Math. 97 (1976) 1029-1047

Explosions in completely unstable flows

Trans. Amer. Math. Soc. 245 (1978) 43-88

Shift automorphisms in the Henon mapping (with R. Devaney)

Commun. Math. Phys. 67 (1979) 137-146

reprinted in:

Hamiltonian Dynamical Systems

R. S. Mackay & J. D. Meiss (eds.)

(Adam Hilger: Bristol & Philadelphia, 1987) pp. 555-565

Non-wandering sets of the powers of maps of the interval (with E. Coven)

Ergodic Theory & Dyn. Syst. 1 (1980) 9-31

Recurrent structure of completely unstable flows on surfaces of finite Euler characteristic

Amer. J. Math. 103 (1981) 143-180

Global structural stability of flows on open surfaces (with J. Kotus & M. Krych)

Memoirs Amer. Math. Soc. v. 37, no. 261 (May, 1982) 104 pp.

Topological dynamics on the interval

in

Ergodic Theory and Dynamical Systems II

A. B. Katok (ed.)

(Birkhauser: Boston & Basel, 1982) pp. 1-73

Differential Equations---A First Course (with M. Guterman)

(Saunders College Publ.)

First ed.: 1984, 651 pp.

Second ed.: 1988, 742 pp.

Third ed.: 1992, 787 pp.

Chaps. 1-5 reprinted (2006) by Indo American Books

Combinatorial patterns for maps of the interval (with M. Misiurewicz)

Memoirs Amer. Math. Soc. v. 94, no. 456 (Nov., 1991) 112 pp.

Braids and the Nielsen-Thurston classification (with D. Benardete & M. Gutierrez)

J. Knot Theory and its Ramifications 4 (1995) 549-618

Preimage entropy of mappings (with F. Przytycki)

Int. J. Bifurcation & Chaos, vol. 9 (1999) pp. 1815-1844

erratum

Hamiltonian stability in the plane (with X. Jarque)

Ergodic Theory & Dyn. Syst. 20(2000) pp. 775-799

Papers and Manuscripts, 2000- :

Crossing matrices and Thurston's canonical form for braids (with J. Burillo, M. Gutierrez & S. Krstic)

Topology and its Applications, vol. 118 (2002) pp. 293-308

Embedding groups of graph automorphisms in surfaces (with J. Los)

Topology 43 (2004) 49-69

Entropy and Preimage Sets (with Doris Fiebig and Ulf-Rainer Fiebig)

Ergodic Theory & Dyn. Syst. 23(2003) 1785-1806

Topological Entropy and the Preimage Structure of Maps

Real Analysis Exchange 29(1) (2003/4) 9-42

Topological Entropy of m-Fold Maps (with J. Bobok)

Ergodic Theory & Dyn. Syst. 25 (2005) 375-401

Topological Entropy of m-Fold Maps on Trees (with J. Bobok)

math arxiv math.DS0609299 (2006)

Ergodic Theory & Dyn. Syst. 27 (2007) 1-31

Topological Entropy for Non-uniformly Continuous Maps (with B. Hasselblatt & J. Propp)

math arxiv math.DS0511495 (2005)

Calculus Deconstructed: A Second Course in First-Year Calculus

Notes for Math 17 (Version of May 27, 2008): 584 pp.

On the Genesis of Symbolic Dynamics as We know It (with E. Coven)

math arxiv math.DS0611322 (2006)

Colloquium Mathematicum 110 (2008) No. 2, 227-242

Note: the version on arxiv does not contain scanned copies

of two letters which are included in the version linked here.