Chaotic orbits in Logistic(Quadratic) Maps Family
As reserchers on mathematical biology, some of you have seen the difference equation Nt+1 = Nt(1 － Nt) (reviewed by May 1976). This equation does look very simple but can never be solved (i.e. it is impossible to get an explicit form of the solution Nt irrespectively of the initial value N0 ∈ I := [0; 1]). However, it is NOT impossible to get a piece of information of such orbits that never go out of the interval I. In this presentation, I’ll demonstrate a topological way of dealing with a dynamical system without proofs and show you an example of hyperbolic set. Moreover, as a equivalent dynamics to this, Symbolic Dynamics is introduced. This idea would be helpful to your analyzing dynamical systems more externally.
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