Media Summary: Let's examine a bit more deeply the kinds of chaos that arise in 1-D discrete time systems. There are other maps that can be fitted with symbolic dynamics, just like we did with the doubling map The logistic map is a great example of how one transitions from simple to chaotic dynamics. In this case, there's a curious pattern ...
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Let's examine a bit more deeply the kinds of chaos that arise in 1-D discrete time systems. There are other maps that can be fitted with symbolic dynamics, just like we did with the doubling map The logistic map is a great example of how one transitions from simple to chaotic dynamics. In this case, there's a curious pattern ... There are some "universal" patterns in the period-doubling route to chaos that we saw in the logistic map. Is there a deep meaning ... Welcome to the "with DA" reading challenge! We'll be reading through the Ellen White's marvelous book on the parables of Jesus ... Let's simulate and see what happens. Oh dear.
We observe that the Lorenz system is chaotic... but what does that mean? It's time at last to begin the analysis of chaotic dynamics. So, what is that? Let's warm-up with a recollection of how we did symbolic dynamics in the context of the doubling map and the tent map. Let's wrap up our proof of chaos in the (geometric) Lorenz system by putting what we know about symbol sequences to work. Our strategy now shifts to a phenomenally important idea: symbolic dynamics. The Lorenz system is the classic model of continuous-time chaos. Let's briefly go over the model and where it comes from.
