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