Question please help 3. Consider the discrete-time dynamical system on X = RP. given by the iteration Xn+1 = A.x,, where A -G :) [4 marks) [10 marks) (a) Determine the stability (unstable, stable, asymptotically stable or globally asymp- totically stable) of the origin (0,0). (b) Determine the corresponding flow operator Sn, ne NO, E ER? (c) Compute all equilibria (fixed points) and all 4-periodic points. Show that the peri- odic points are dense and sketch the dynamics in the phase space. (d) Show that the map has no sensitive dependence on initial conditions. Hint: Show that ||xn+1 || = ||xn||, i.e. || 4.4|| = ||«l], where 11611 = +€ (e) is the map chaotic? Prove your answer. 16 marks) [8 marks [2 marks

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Transcribed Image Text: 3. Consider the discrete-time dynamical system on X = RP. given by the iteration Xn+1 = A.x,, where A -G :) [4 marks) [10 marks) (a) Determine the stability (unstable, stable, asymptotically stable or globally asymp- totically stable) of the origin (0,0). (b) Determine the corresponding flow operator Sn, ne NO, E ER? (c) Compute all equilibria (fixed points) and all 4-periodic points. Show that the peri- odic points are dense and sketch the dynamics in the phase space. (d) Show that the map has no sensitive dependence on initial conditions. Hint: Show that ||xn+1 || = ||xn||, i.e. || 4.4|| = ||«l], where 11611 = +€ (e) is the map chaotic? Prove your answer. 16 marks) [8 marks [2 marks

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Hey, seems your question is not posted completely. If you have posted a pic, then it happens sometimes due to glitch that picture doesn't get uploaded, to fix this just logout and login your ID again, so it won't happen again from next time. I'm attaching a screenshot, as this is how your question is appearing: CheggHomeExpert Q&A My answersTime remaining: 01:59:56Algebraplease helpYour answerTyped answers are easier for students to read than handwritten notes\min ^{2 \pi} This could be marked as Spam. Any query please ask in comments. ...