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Answers
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3
Is there a dynamical system such that every orbit is either periodic or dense?
0
Supremum amongst Kolmogorov-Sinai entropies: ergodic or just invariant measures.
4
Invariant measures and recurrent sets.
1
Is the composition of non-wandering maps still non-wandering?
1
Conley Theorem (or fundamental theorem of dynamical systems)
0
probability measures with entropy equal to nonnegative number
2
The Manneville-Pomeau map is topologically conjugate to a full one-sides shift on two symbols. Can you give the corresponding homeomorphism?
3
Hyperbolic sets
1
Hyperbolic sets that are not locally maximal