2010-2011 UF Graduate Catalog (PDF Format) - Graduate School ...

University of Florida Graduate School
http://test.gradschool.ufl.edu/catalog/current-catalog/FOI/MS01.htm[9/15/2010 4:07:59 PM]
MTG 5317: Introduction to Topology II (3) Prereq: MTG 5316.
MTG 5411: Introduction to Fractal Geometry (3) Prereq:
advanced calculus or consent of instructor. Introduction to
techniques for generating and analyzing fractal sets. Hausdorff
dimension, self-similarity, and iterated function systems. If time
permits, Brownian paths, Julia sets, and Mandelbrot set.
MTG 5412: Introduction to Dynamical Systems and Chaos (3)
Prereq: advanced calculus or consent of instructor. Introduction to
nonlinear dynamical systems and chaos. One-dimensional systems,
bifurcation theory, symbolic dynamics, Sarkovskii's theorem,
Schwarzian derivative, Bernoulli shifts and subshifts of finite type,
and kneading theory. If time permits, toral automorphisms, Henon
map and complex dynamics.
MTG 6256: Differential Geometry I (3) Prereq: consent of
instructor. Foundations of the theory of smooth manifolds, vector
fields, and differential forms. Topics chosen from a list including
differential topology, Lie groups, symplectic geometry, Riemannian
geometry, and applications to physics.
MTG 6257: Differential Geometry II (3) Prereq: MTG 6256.
MTG 6346: Topology I (3) Prereq: MTG 5317. A basic introduction
to advanced topology. Topics covered include general topology,
algebraic topology, homotopy theory and topology of manifolds.
MTG 6347: Topology II (3) Prereq: MTG 6346.
MTG 6401: Ergodic Theory and Dynamical Systems I (3)
Prereq: MTG 5317, MAA 6617, or consent of instructor. Periodic
points, recurrence, nonwandering and chain recurrent sets,
topological conjugacy, minimal sets. Topological entropy, metric
entropy. Measure preserving transformations, ergodicity, mixing.
Birkhoff's ergodic theorem. Bernouilli shifts. Anosov
diffeomorphisms, structural stability, hyperbolic sets. Basic sets,
symbolic dynamics, Markov partitions. Lyapunov exponents, KAM
(Kolmogorov, Arnold, Moser) theory.
MTG 6402: Ergodic Theory and Dynamical Systems II (3)
Prereq: MTG 6401. Continuation of MTG 6401.
MTG 7396: Advanced Topics in Topology I (3; max: 6) Prereq:
MTG 6347. Topics change yearly.
MTG 7397: Advanced Topics in Topology II (3; max: 6)
The University of Florida is accredited by the Commission on Colleges of the Southern Association of Colleges and Schools (1866 Southern Lane, Decatur,
Georgia 30033-4097; telephone number 404 679 4501) to award associate, bachelor's, master's, doctoral, specialist, engineer and professional degrees.