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Chaotic Dynamical System

By Prof. Anima Nagar   |   IIT Delhi
Learners enrolled: 336
The aim of this course is to provide insight into elementary topics and current studies in the theory of chaotic dynamical systems. The focus will be on providing the students with basics in the area and introduce them to the fundamentals in this field. This course discusses the various definitions of Mathematical Chaos in elementary analytical way.


INTENDED AUDIENCE :Researchers, Senior undergraduates, Post graduates
PREREQUISITES : A good course in Real Analysis, Metric Spaces.l
INDUSTRY SUPPORT : None
Summary
Course Status : Completed
Course Type : Elective
Duration : 12 weeks
Category :
  • Mathematics
Credit Points : 3
Level : Undergraduate/Postgraduate
Start Date : 27 Jan 2020
End Date : 17 Apr 2020
Enrollment Ends : 24 Feb 2020
Exam Date : 25 Apr 2020 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.


Page Visits



Course layout

Week 1  :  Analysis of the dynamics
Week 2  :  Dynamics of one-dimensional maps of both the interval and the circle
Week 3  :  Recurrence and minimality
Week 4  :  Elementary bifurcations
Week 5  :  Sarkovski’s theorem
Week 6  :  Li Yorke chaos and Scrambled sets
Week 7  :  ATransitivity and Devaney Chaos
Week 8  :  Stronger forms of Transitivity
Week 9  :  Symbolic Dynamics
Week 10  :Topological Entropy
Week 11  : Higher Dimensional Dynamics
Week 12  : Toral Automorphisms and Henon Map

Books and references

1. DISCRETE CHAOS: Saber Elaydi,Chapman & Hall/CRC, II Edition, 2007.
2. CHAOS: AN INTRODUCTION TO DYNAMICAL SYSTEMS: Alligood, Yorke, Sauer, Springer, 2003.
3. AN INTRODUCTION TO CHAOTIC DYNAMICAL SYSTEMS: Bob Devaney,Addison-Wesley, 1998.
4. A FIRST COURSE IN DYNAMICS: Boris Hasselblatt and Anatole Katok, C.U.P., ICM 2010 series, 2010.

Instructor bio

Prof. Anima Nagar

IIT Delhi
The instructor is a faculty at the Mathematics Dept. of IIT Delhi. Her primary area of research is in Topological Dynamics.

Course certificate

• The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
• The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 25th April 2020, Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
• Registration url: Announcements will be made when the registration form is open for registrations.
• The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
• Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE:
• Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments
 given in the course. 
• Exam score = 75% of the proctored certification exam score out of 100
• Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. 
• If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.
• Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras. It will be e-verifiable at nptel.ac.in/noc.
• Only the e-certificate will be made available. Hard copies will not be dispatched.


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