Lecture 10 - Some of the objects of dynamics

So for today, we will continue to take some time to introduce and study some of the objects of dynamics that go beyond maps and ODEs.  Mainly, some common spaces that act as domains for maps, or the places that serve as playgrounds for orbits and trajectories.  It turns out that the properties of a dynamical system do not only rely on the properties of a map, but also on the properties of the domain of a map.

Once we define a couple more things like isometries and equivalence of metrics, we will define a few spaces that we will study more closely later, like spheres and tori.  We will spend some time on the simple space of a circle, since defining it will be important to understanding it.  And we will also define a new space, useful in dynamics and weirdly mesmerizing in analysis in general;  The Cantor Set.   Most likely,m we will end here.

See you today.

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