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Swayam Central

Chaotic Dynamical System

By Prof. Anima Nagar   |   IIT Delhi
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

Learners enrolled: 161

SUMMARY

Course Status : Upcoming
Course Type : Elective
Duration : 12 weeks
Start Date : 27 Jan 2020
End Date : 17 Apr 2020
Exam Date : 25 Apr 2020
Enrollment Ends : 03 Feb 2020
Category :
  • Mathematics
  • Level : Undergraduate/Postgraduate
    This is an AICTE approved FDP course

    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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