6 problems

Let $f$ and $g$ be topologically conjugate one-dimensional maps, and let $x$ be a point of $f$ that is not attracted to a periodic orbit. The upper pointwise Lyapunov exponent of…

Consider a generic one-parameter family of maps. Density conjecture. Maps with exponential decay of correlations are Lebesgue density points of other maps with uniform exponential…

A multimodal Collet–Eckmann map is a multimodal interval map satisfying the Collet–Eckmann condition, and strong stochastic stability means stability of its statistical behaviour u…

Let $f$ and $\tilde f$ be maps in the setting of the main theorems, and let $c$ be a critical point. Write $\omega(c)$ for the omega-limit set of $c$, and call it of bounded geomet…

Periodic-attractor bound. There exists a neighbourhood ${\cal F} \subset C^3({\cal N})$ of $f$ such that for any $g\in {\cal F}$ the number of periodic attractors of $g$ is bounded…

Suppose a topological class of one-dimensional maps consists of maps with one critical value, and suppose that, for each critical exponent in a sequence tending to $\infty$, limits…