I was reading "Prove that Anosov Automorphisms are chaotic," and the answer and a few of the comments talked about orbits. I'm curious what is meant by "orbits" in the given context. Is it analogous to transformations?
What is meant by "orbit" in this question?
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linear-algebra
soft-question
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0This is the usual meaning: https://en.wikipedia.org/wiki/Group_action#Orbits_and_stabilizers – 2012-12-03
1 Answers
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Given a set $S$, a function $f:S\to S$, and an element $x$ in $S$, the orbit of $x$ is the set $\{{\,x,f(x),f(f(x)),f(f(f(x))),\dots\,\}}$