Question: Consider the tent map on R defined by In In+1 3(1 - In) In > (a) Find the set of initial conditions ro E [0,

Consider the tent map on R defined by In In+1 3(1 - In) In > (a) Find the set of initial conditions ro E [0, 1] satisfying 1 E [0, 1]. That is, after one iteration the dynamics remains in the interval [0, 1]. (b) Describe the set of points ro E [0, 1] satisfying 12 E [0, 1]. (c) Describe the set of points that never escape the interval [0, 1]. That is the set I defined by I = {ro E [0, 1] : Vn E N, In E [0, 1]}. (d) Prove that I is uncountable

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