Tentative Calendar for Math A4500, Section ST, Fall 2022

This calendar is extremely tentative, but should give a general idea of what topics we will cover.

Course Textbooks:

Date Tentative class plan:
Thu, Aug 25 Introduction to dynamical systems (roughly following Devaney's I.1-I.2).
Introduction to topological conjugacy. (Not introduced in the book until Devaney I.7).
Tue, Aug 30 Examples of Dynamical Systems (perhaps different than Devaney I.2).
Devaney A.1: Preliminaries from Calculus.
Devaney A.2: Preliminaries from Geometry and Topology.
Devaney I.3: Elementary Definitions.
A note clarifying definitions of forward asymptotic.
Thu, Sep 1 Devaney I.4: Hyperbolicity.
Tue, Sep 6 Conjugacy in homeomorphisms.
Start Devaney I.5: The Logistic Family of Maps.
Thu, Sep 8 Continue Devaney I.5: The Logistic Family of Maps.
Discuss Cantor Sets.
Tue, Sep 13 Devaney I.5: The Logistic Family of Maps.
Thu, Sep 15 Class held in NAC 1/511.
Finish Devaney I.5: The Logistic Family of Maps.
Experimenting with dynamics of functions using Sage.
Tue, Sep 20 Class held in NAC 1/511.
Review for the midterm.
Thu, Sep 22 Midterm 1.
Tue, Sep 27 No classes scheduled
Thu, Sep 29 No class (Classes follow a Monday schedule)
Tue, Oct 4 No class scheduled
Thu, Oct 6 Devaney I.6: Symbolic Dynamics.
Tue, Oct 11 Devaney I.7: Topological Conjugacy.
Thu, Oct 13 Semiconjugacy (from the end of section I.7).
Tue, Oct 18 Devaney I.9: Structural Stability.
Thu, Oct 20 Devaney I.8: Chaos.
Tue, Oct 25 Devaney I.10: Sharkovsky’s Theorem.
Thu, Oct 27 Devaney I.10: Sharkovsky’s Theorem.
Devaney I.10: Sharkovsky’s Theorem.
Tue, Nov 1 Devaney I.11: The Schwarzian Derivative.
Thu, Nov 3 Midterm 2.
Tue, Nov 8 Finish Devaney I.11: The Schwarzian Derivative.
Thu, Nov 10 Devaney I.12: Bifurcations.
Tue, Nov 15 Devaney III.28: The Smale Horseshoe Map.
Please read Devaney III.27: Dynamics of Linear Maps.
Thu, Nov 17 Devaney I.16: Maps of the Circle.
Tue, Nov 22 Devaney III.29: Hyperbolic Toral Automorphisms.
Lecture posted on blackboard due to illness..
Thu, Nov 24 College closed (Happy Thanksgiving!)
Tue, Nov 29 Continue Devaney I.16: Maps of the Circle.
Begin discussing Poincaré's Theorem for circle homeomorphisms.
Thu, Dec 1 Finish Devaney I.16: Maps of the Circle.
Tue, Dec 6 Devaney III.30: Attractors.
Thu, Dec 8 Finish Devaney III.30: Attractors.
Discuss Markov Partitions in the context of toral automorphisms and the solenoid..
Tue, Dec 13 Midterm 3.

The Final Presentation will be held when the final exam is scheduled by the college: Tuesday, December 20th from 6pm to 8:15pm.


Relevant links:
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Last modified on December 6, 2022.
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