Lyapunov Exponents - Dynamical Systems | Lecture 31

A hallmark of chaos is "sensitive dependence on initial conditions", which roughly states that trajectories that start close together must eventually separate. The classical way to measure if a system has such a sensitive dependence is through the Lyapunov exponent. In this lecture we define the Lypaunov exponent and work through an example on the tent map. In practice this exponent is something that can't be determined analytically but is often left to the computer. Such a computational process is also described in this lecture.

This course is taught by Jason Bramburger for Concordia University.

Follow @jbramburger7 on Twitter for updates.

[michaelzumpano]

This is the first of your videos that I’ve watched. It is very clear and easy to follow. I’ll back up and watch the series from the beginning. Excellent work!

[scraps]

These videos are incredibly interesting, thanks for your work!

[ogunstega]

at 2:23 you said it is quite easy to do this for discrete dynamical systems, my question does this same approach for computing the Lyapunov exponents works for continuous dynamical systems? Thanks

[maggie]

quick question, why take the limit as n -> infinity for the lyapunov exp? is it just to satisfy the equality of delta n = delta 0 e^lambda*n? because I thought there can be many lyapunov exponents for a given dynamical system.

[SaurabhSharma-suyx]

What is the name of theorem that you mentioned at @5:31?

[vivekdixit]

Nice explanation! If we have a time series data point i.e. (t, x) where x is the signal and t is the time. Can we get the Lyapunov exponent for this ?

[md.sarowarhossainrana]

How to find lyapunov exponent for 3D continuous model?

[bugginfelix]

Can I send you an equation for this and other subject pertaining to black hole science? I’m a novice but I need someone to look at this and tell me if it’s important.

[andrejgrebenc]

Pls pronounce Lyapunov with the accent on "u" not on "a"!!!!

[SaurabhSharma-suyx]

What is the name of theorem that you mentioned at @5:31?