ONLINE COURSE!

http://dynamics.mi.fu-berlin.de/lectures/20WS-Fiedler-Lopez-DynamicalSystems2/index.php

Tuesday and Thursday 10:15-12:00

Lecture Zoom-Meeting link 

Meeting-ID: 842 7802 3965 Pass: dyn2020

Live classes will take place via Zoom. Additional materials will be provided for download. 

Pass Criteria
Solve correctly at least 25% of the assignments. Hand in solution attempts for at least 50% of the assignments. 
Present a correct solution to an assignment on the blackboard in the recitation session at least once. 
Pass the written exam. 

Written Exam

The written exam will take place on Tuesday February 23, 10:00-12:00 Berlin time. More information on the specific format can be found here, make sure to read it carefully!

Resit Exam (Nachklausur)

The written exam will take place on Tuesday April 13, 10:00-12:00 Berlin time. We will follow the same procedure we had for the first exam, more information can be found here, make sure to read it carefully!

Audience
Students of mathematics or physics, including teachers, from semester 3.

Direct access to thesis projects: bachelor, master, dissertation. 

Students interested in dynamical systems are also welcome to participate in the seminar 

(Hi)stories of Dynamics 2

Topics
Dynamical Systems are concerned with anything that moves. 
Through the centuries, mathematical approaches take us on a fascinating voyage from origins in celestial mechanics to contemporary struggles 
between chaos and determinism.

The three semester course, aimed at graduate students in the framework of the Berlin Mathematical School, 
will be mathematical in emphasis. Talented and advanced undergraduates, however, are also welcome to this demanding course, as are students from the applied fields, 
who plan to really progress to the heart of the matter.


Here is an outline of the first semester: Last semester

  1. Existence and uniqueness of solutions of ordinary differential equations
  2. Flows, differentiablility and first integrals 
  3. Linear differential equations
  4. Omega-limit sets and Lyapunov functions
  5. Planar flows and the Poincaré-Bendixson theorem
  6. Forced oscillations 

Semester 2:

  1. Autonomous and forced oscillations
  2. Torus flows
  3. Stable and unstable manifolds
  4. Shift dynamics
  5. Hyperbolic sets
  6. Center manifolds
  7. Normal forms
  8. Genericity and Takens embedding

References

  • K.T. Alligood, T.D. Sauer and J.A. Yorke: Chaos, Springer, 1997.
  • H. Amann: Ordinary Differential Equations, de Gruyter, 1990.
  • V.I. Arnold: Ordinary Differential Equations, Springer, 2001.
  • V.I. Arnold: Geometrical Methods in the Theory of Ordinary Differential Equations, Springer, 1988.
  • W.E. Boyce and R.C. DiPrima: Elementary Differential Equations and Boundary Value Problems, Wiley, 5th edition, 1992.
  • S.-N. Chow and J.K. Hale: Methods of Bifurcation Theory, Springer, 1982.
  • E.A. Coddington and N. Levinson: Theory of ordinary differential equations, McGill-Hill, 1955.
  • P. Collet and J.-P. Eckmann: Concepts and Results in Chaotic Dynamics. A Short Course, Springer, 2006.
  • R. Devaney, M.W. Hirsch and S. Smale: Differential Equations, Dynamical Systems, and an Introduction to Chaos, Academic Press, 2003.
  • Dynamical Systems I, D.K. Anosov and V.I. Arnold (eds.), Encyclopaedia of Mathematical Sciences Vol 1, Springer, 1988.
  • J. Hale: Ordinary Differential Equations, Wiley, 1969.
  • B. Hasselblatt, A. Katok: A First Course in Dynamics, Cambridge 2003.
  • P. Hartmann: Ordinary Differential Equations, Wiley, 1964.
  • A. Katok, B. Hasselblatt: Introduction to the Modern Theory of Dynamical Systems, Cambridge 1997.
  • F. Verhulst: Nonlinear Differential Equations and Dynamical Systems, Springer, 1996.
  • E. Zeidler: Nonlinear Functional Analysis and its Applications, Volume 1: Fixed-Point Theorems, Springer, 1998.

Discord Informal Dynamics link

Tutorials

Wednesdays 16:00-18:00 via Zoom (link)

Meeting ID: 361 072 2559
Passcode: dyn2020

Please make sure that you have a working microphone, and at best, the possibility to share the screen as well as a webcam.

Homework assignments
Form teams of two, work on four problems per week, submit at least two, get one right each week (on average). Submission procedure: email a .pdf or .jpg file of your solutions to your assigned tutor, before the deadline. Be prepared to explain any of your solutions (no matter whether your own or the solution by your team partner!) during any tutorial, live.  

Please send your solutions to the following address: dynamics.exercises@gmail.com.

Assignment, due 19.11.2020 PDF

Assignment, due 26.11.2020 PDF

Assignment, due 3.12.2020 PDF

Assignment, due 10.12.2020 PDF

Assignment, due 17.12.2020 PDF

Christmas exercises, due 11.01.2021 PDF

Assignment, due 21.01.2021 PDF

Assignment, due 28.01.2021 PDF

Assignment, due 04.02.2021 PDF

Assignment, due 11.02.2021 PDF

Assignment, due 18.02.2021 PDF

Basic questions

Questions 1 

Questions 2