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The first question asks, How many unstable periodic orbits are there in the dynamical landscape of a dissipative chaotic system?
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From the lecture, we know that there are unstable periodic orbits of every period present in the dynamical landscape of a dissipative chaotic system
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If theres an unstable periodic of every orbit, this means that there must be an infinite number of unstable periodic orbits
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Question 2 asks if all UPOs have even-numbered periods, and this is false
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In the dynamical landscape of dissipative chaotic system, for example, there are unstable periodic orbits of every period
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That is, if you pick any natural number, theres an unstable periodic orbit of that period
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The final question asks, Which of the following statements are true about the relationship between unstable periodic orbits and chaotic attractors?
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From lecture we know that a chaotic attractor is the closure of the set of its unstable periodic orbits, and that the unstable periodic orbits are dense in any chaotic attractor
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So both of the above are true