METEO 597 Nonlinear Dynamics and Chaos, Spring 2019

Instructor: John Harlim Office: McAllister 214
Phone: 814-863-9024
Email : [email protected]
Office hours: Wednesday 2-4 PM or by appointment

Time and Place: TR 1.35-2.50, Osmond Lab 116
Prerequisites: Basic Calculus/Analysis, Linear Algebra/Matrix Theory, and Ordinary/Partial Differential Equations.

 

Topics: This course will cover basic topics in discrete and continuous dynamical systems, including maps and ordinary differential equations, linear and nonlinear stability analysis, bifurcations, characterization of chaos using Lyapunov exponents, fractal and correlation dimensions. If time is permitted, we will discuss a characterization of dynamical systems using the empirical measure defined through the maximum entropy principle and equilib- rium statistical mechanics theory. Application on basic geophysical dynamics, the barotropic quasi-geostrophic equation with topographic stress smaller scale interaction with a large scale mean flow, will be discussed.

 

Grades: Grades will be based on homework (30%) and reading assignments/class presen- tations on relevant topics (70%). Several homework problem sets will be assigned to ensure that you are engaged on the topics covered in the class. I will assign some reading materials and ask you to do class presentations. Depending on the class size, each student may do more than one oral presentation.

 

Academic Integrities: All Penn State Policies apply to this course, including Academic Integrity. See the following website for these policies. http://www.psu.edu/ufs/policies/ and http://www.science.psu.edu/academic/Integrity/index.html

 

Students with Dissabilities: Penn State welcomes students with disabilities into the University’s educational programs. If you have a disability-related need for modifications or reasonable accommodations in this course, contact the Office for Disability Services, ODS is located in room 116 Boucke Building, For further information regarding ODS, please visit their website at http://www.equity.psu.edu/ods/

 

Text: The lecture is prepared from the text [1] and [2]. The remaining references are for further readings.

References

[1] K.T. Alligood, T.D. Sauer, and J.A. Yorke. Chaos: An Introduction to Dynamical Sys- tems, Springer, 1996.
 
[2] A.J. Majda and X. Wang. Nonlinear Dynamics and Statistical Theories for Basic Geo- physical Flows, Cambridge University Press, 2006.

 

[3] R.L. Devaney. An Introduction to Chaotic Dynamical Systems, 2nd edition, Addison- Wesley, 1989.

 

[4] S.H. Strogatz. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Westview Press, 2001.