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October 19, 2022

Consider the h’la.rotta"’s map In+1 2 ﬁr”) :2 (1331(1 — on}. a)

Consider the h’la.rotta"’s map In+1 2 ﬁr”) :2 (1331(1 — on}. a) Find all the ﬁxed (equilibrium) points as a function of a and determine their stability depending on a. b} Find and classify all points of bifurcations from the equilibrium points. c) Find a formula. for the branch of period ‘2 orbits. d} Plot a. partial bifurcation diagram for this map. Indicate the equilibrium points: the period 2 orbits, their stability5 and bifurcation points. e) (Bonus) Explore the map numerically. Do you suspect chaos for any parameter values? Provide numerical or any other evidence for your answer.

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