7 problems

The one-dimensional logistic map is … with parameter values in the chaotic regime including $\lambda=3.57,\ldots,4$, and its iterates define a sequence by $x_i=f_\lambda(x_{i-1})$.…

Galatolo et al.'s conjecture. The bound $|\Gamma^{-}|\geq 0.0455$ is very close to the actual measure $|\Gamma^{-}|$. The conjecture concerns how much of the regular-parameter set…

Maximum-period conjecture. When $\mu\bmod 3=1$, the maximum period is

Let $\rho$ be a positive integer, let $\bar{\lambda}$ be the average parameter value, and let $p_i(\bar{\lambda})$ for $1\leq i\leq 2^\rho$ denote the stable period-$2^\rho$ points…

Logistic-map conjecture. In the case of the logistic map, the emergence of fractal structures is connected with the existence of branching points in the Hamiltonian deformation fun…

Let $x_{\alpha,\varepsilon}$ be the invariant curve obtained by continuation of the invariant curve $x_{\alpha,0}(\theta)=1-1/\alpha$ for $\varepsilon>0$. The constraints described…

Let $K$ be the carrying capacity, $r$ the growth parameter, and $\tau$ a nonnegative integer time delay. Consider the delayed logistic recurrence … For a fixed delay, write the two…