|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||§ 1.5: An example: the quadratic family.
|Wed, Feb 13||§ 1.5: An example: the quadratic family.
|Mon, Feb 18||No class: CCNY is closed.|
|Wed, Feb 20||§ 1.6: Symbolic Dynamics.
|Mon, Feb 25||§ 1.6: Symbolic Dynamics.
|Wed, Feb 27||First Midterm.|
|Mon, Mar 4||§ 1.7: Topological Conjugacy.
Please read § 1.8: Chaos.
§ 1.9: Structural Stability.
|Wed, Mar 6||§ 1.10: Sharkovskys Theorem.
|Mon, Mar 11||§ 1.10: Sharkovskys Theorem.
|Wed, Mar 13|
|Mon, Mar 18|
|Wed, Mar 20|
|Mon, Mar 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.
|Wed, Mar 27||Discussed § 2.3: The Horseshoe Map
|Mon, Apr 1||Second Midterm.|
|Wed, Apr 3||Finish discussion of the Horsehoe map. Begin discussion of linear maps following § 2.1 and § 2.2.
|Mon, Apr 8||§ 2.4: Toral automorphisms.
|Wed, Apr 10|
|Mon, Apr 15|
|Wed, Apr 17|
|Mon, Apr 22||Spring break|
|Wed, Apr 24||Spring break|
|Mon, Apr 29|
|Wed, May 1|
|Mon, May 6|
|Wed, May 8|
|Mon, May 13||Third Midterm.|