Tentative Calendar for Spring 2019

This calendar is subject to change, but should give a general idea of when we will cover certain topics.
 Date Tentative class plan: Mon, Jan 28 A broad introduction to dynamical systems (roughly following Devaney's § 1.1) Wed, Jan 30 § 1.2: Preliminaries from Calculus. Discusion of rotations of the circle. § 1.3: Elementary definitions. Mon, Feb 4 Worked through Sage notebooks related to topics covered so far. Wed, Feb 6 More discussion of homeomorphisms of R. Introduction to topological conjugacy. (Not introduced in the book until § 1.7). § 1.4: Hyperbolicity. Mon, Feb 11 § 1.4: Hyperbolicity. Wed, Feb 13 § 1.5: An example: the quadratic family. Mon, Feb 18 No class: CCNY is closed. Wed, Feb 20 § 1.5: An example: the quadratic family. Mon, Feb 25 § 1.6: Symbolic Dynamics. Wed, Feb 27 First Midterm. Mon, Mar 4 Snow day: CCNY was closed. Wed, Mar 6 § 1.6: Symbolic Dynamics. Mon, Mar 11 § 1.6: Symbolic Dynamics. § 1.7: Topological Conjugacy. Wed, Mar 13 § 1.7: Topological Conjugacy. § 1.9: Structural Stability. Mon, Mar 18 § 1.8: Chaos. § 1.10: Sharkovskys Theorem. Wed, Mar 20 § 1.10: Sharkovskys Theorem. Mon, Mar 25 § 1.11: The Schwarzian Derivative. Wed, Mar 27 Review for midterm 2. Mon, Apr 1 Second Midterm. Wed, Apr 3 § 1.12: Bifurcations Mon, Apr 8 § 1.13: Shifts of finite type § 2.1: Preliminaries. (In particular Brouwer's Fixed Point Theorem and the Contraction Mapping Theorem.) You will want to read the rest of the section. Wed, Apr 10 Discussion of linear maps following § 2.1 and § 2.2. Again, our discussion will be incomplete, you will want to read the section. § 2.3: The Horseshoe Map Mon, Apr 15 Finish discussion of the Horsehoe map. Wed, Apr 17 § 2.4: Toral automorphisms. Mon, Apr 22 Spring break Wed, Apr 24 Spring break Mon, Apr 29 Complex Dynamics (Prof. Merenkov) Wed, May 1 Complex Dynamics (Prof. Wolf) Mon, May 6 § 2.4: Toral automorphisms and Markov Partitions. § 2.5: Attractors, with an emphasis on the Solenoid Wed, May 8 § 2.6: The stable and unstable manifold theorem Mon, May 13 Wed, May 15 Third Midterm.

Final presentations will be held when our final exam is scheduled: 1-3:15pm on Wednesday, May 22nd.