14 problems

Let $T\colon X \to X$ be a smooth diffeomorphism of a compact Riemannian manifold $X$ with a natural measure $\mu$ of information dimension $\operatorname{ID}(\mu)=D$. An observabl…

Second minimal odd-orbit digraph conjecture. For every integer $k\geq 3$, the digraph of any second minimal $(2k+1)$-orbit has one of $4k-3$ possible types up to inverses.

A robust chaos conjecture asserts that chaos is a robust, high-probability behavior for high-dimensional, bounded, nonlinear dynamical systems. The paper reports near-unity experim…

Let $f$ be a mapping (neural network) and let $U$ be a bifurcation chain set as in the hyperbolicity violation conjecture. The periodic-window probability conjecture asserts that,…

Let a Hamiltonian dynamical system exhibit mixed chaos, with chaotic trajectories and islands of regularity in its phase space. Suppose the system is weakly coupled to a thermal ba…

Let $T_0$ and $T_t$ be the passage times at perturbation times $0$ and $t$, and write $\operatorname{Var}(T)$ for the variance of the passage time and…

Let ${\cal M}({\cal E})=\{({\rm r},{\rm G},{\rm g}):{\rm E}({\rm r},{\rm G},{\rm g})={\cal E}\}$ be the lifted level manifolds of the Euler integral, and let…

Let $v\in(0,1/2)$, and let the Kasner circle eIFS be the iterated function system consisting of the maps ${\cal K}_{\mu\nu\zeta}:\mathrm{K}^{\ocircle}\to\mathrm{K}^{\ocircle}$ defi…

Consider a commensurate fractional-order system … with threshold value $\alpha_t$, and let $\bar{\alpha}$ be the maximum stability bound $\alpha_*(E)$ over the equilibrium points a…

Consider a nonlinear autonomous system … whose second-order form is … so that the functions $g_i$ act as oscillator frequencies and the functions $h_i$ are the remaining terms. Com…

Let … be the rational map associated with parameters $\alpha$, $\beta$, $\gamma$, and $\delta$. A chaotic trajectory is called fractal-like or fractal-unlike according to the obser…

Let $({\cal P}_0)$ be the discretized nonlinear algebraic problem associated with a nonlinear dynamical system, and let $({\cal P})$ be the corresponding optimization problem with…

Consider the difference equation … Here $\alpha$ and $\beta$ are complex parameters, and a solution is called chaotic in the sense used by the paper's numerical dynamical analysis.…

Let $X$ be a totally regular continuum, meaning a continuum in which every two points can be joined by an arc of finite length. Write $I^{\operatorname{ED}}(X)$ for the infimum of…