|Date||Tentative class plan:|
|Tue, Jan 31||A broad introduction to dynamical systems
|Thu, Feb 2||§ 1.3: Elementary definitions.
Demonstration of some other dynamical systems.
|Tue, Feb 7||§ 1.2: Preliminaries from Calculus.
Discusion of rotations of the circle.
|Thu, Feb 9||Snow day (A makeup was scheduled by the college).|
|Tue, Feb 14||§ 1.4: Hyperbolicity.
Introduction to topological conjugacy. (Not introduced in the book until § 1.7).
|Thu, Feb 16||§ 1.4: Hyperbolicity.
|Tue, Feb 21||§ 1.5: An example: the quadratic family.
|Thu, Feb 23||§ 1.5: An example: the quadratic family.
|Tue, Feb 28||First Midterm.|
|Thu, Mar 2||§ 1.5: An example: the quadratic family.
|Tue, Mar 7||§ 1.6: Symbolic Dynamics.
|Thu, Mar 9||§ 1.6: Symbolic Dynamics.
|Tue, Mar 14||Snow day (Smale's Lecture served as the makeup).|
|Thu, Mar 16||§ 1.7: Topological Conjugacy.
Please read § 1.8: Chaos.
§ 1.9: Structural Stability.
|Tue, Mar 21||§ 1.10: Sharkovskys Theorem.
|Thu, Mar 23||§ 1.10: Sharkovskys Theorem.
|Tue, Mar 28|
|Thu, Mar 30|
|Tue, Apr 4|
|Thu, Apr 6||Second Midterm.|
|Tue, Apr 11||Spring break|
|Thu, Apr 13||Spring break|
|Tue, Apr 18||Spring break|
|Thu, Apr 20||No class: CCNY Classes follow Monday Schedule|
|Tue, Apr 25||Discussed some of § 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.
|Thu, Apr 27||Discussed § 2.3: The Horseshoe Map
|Tue, May 2||Finish discussion of the Horsehoe map. Begin discussion of linear maps following § 2.1 and § 2.2.
|Thu, May 4||§ 2.4: Toral automorphisms.
|Tue, May 9|
|Thu, May 11|
|Tue, May 16|
|Thu, May 18||Third Midterm.|
|Fri, May 19||Make-up class. We'll have meetings about the presentations.