4 problems

Let $C^r([0,1])$ denote the space of $C^r$ interval maps. For a generic $k$-parameter family $(f_t)_{t\in[-1,1]^k} \subset C^r([0,1])$, where $t\in[-1,1]^k$ is equipped with Lebesg…

Bogatyi–Shavgulidze conjecture. For every covering system $(I_1,\ldots,I_k;f)$, there exists $x_0\in I_1\cup\cdots\cup I_k$ and an integer $l\leq k$ such that

Fix $m\geq 2$, and let $f_1,f_2\in\operatorname{PA}(m)$ be $m$-modal standard PCP zig-zags of pseudo-Anosov type. Let $\lambda_i$ be the growth rate of $f_i$, and let…

Let $f:[0,1]\to[0,1]$ be continuous. A special $\alpha$-limit set $s\alpha(x)$ is the union of the accumulation-point sets of all backward orbit branches of $x$. Kolyada–Misiurewic…