Suppose we iterate a continous (possibly non linear) map $f:X\rightarrow X$ with $X$ compact metric space and consider the omega limit set of a point $x$ under the iteration of $f$ denoted as $\omega(x)$. Suppose that the map admits (uncountably) infinitely many fixed points and (uncountably) infinitely many periodic points of period 2. Is it possible for some $x$ that $\omega(x)$ contains more than one such limit cycles?
2026-04-05 07:19:44.1775373584
Number of limit cycles in discrete time omega limit set
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