21 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 $x_i=f_\lambda(x_{i-1})$.…

Let $x^{(\epsilon)}_{(\delta)}$ be the forced subsystem driven by a chaotic forcing, with a chaotic subsystem satisfying moderate assumptions and with sufficiently large time-scale…

Evolution-operator learning conjecture. The model's success in forecasting dynamics, including dynamics outside its training data, stems from learning the discrete evolution operat…

Consider an oligopoly game with uncertainty, in which the firms face uncertainty as in the paper's duopoly setting and there are more than three competitors. Extension of Theochari…

A vacillator is a swarmalator trapped between two large anti-phase clusters, typically undergoing coupled spatial and phase oscillations. In the configuration described, the vacill…

The system is a $\mathbb{Z}_2$-equivariant dynamical system with a codimension-two Belyakov homoclinic bifurcation at the point $\textbf{BV}$. The homoclinic orbits in its unfoldin…

SyCo-AE conjecture. The full-space constraint can be approximated by

Unstable-contribution reduction conjecture. The unstable contribution could potentially be reduced if the effect of the larger components of the measure gradient is eliminated.

Monotonicity conjecture. Separation of the Lyapunov exponents implies that the measure-gradient norms increase monotonically when the directions are ordered from the most to the le…

Alignment conjecture. If $J$ is aligned with the most expansive direction of the unstable manifold and the positive part of the Lyapunov spectrum is not clustered around a certain…

Lyapunov-spectrum conjecture. The measure change along $q^1$ is expected to be the smallest, while the measure change along $q^m$ is expected to be the largest.

Alignment constraint conjecture. The alignment constraint is not an obstacle for higher-dimensional systems with statistical homogeneity.

A dynamical system is said to have compact solutions with a low number of unstable directions when its relevant solutions remain compact and the number of unstable directions is sm…

Neural-network conjecture. By using the neural network architecture developed in this manuscript, one will be able to reach conclusions similar to those obtained by computer-assist…

Conjecture on chaotic aperiodic solutions. As limits of sequences of periodic solutions corresponding to finite sequences $(\omega_h)_{h=1}^N$ with $N\to\infty$, there exist chaoti…

Chaoticity-preservation conjecture. The system's chaoticity should be maintained especially well in larger RNNs even after innate training, as indicated by persistently positive ML…

Let ${\vec x}_0(\varphi)$ be a trajectory on a uniformly hyperbolic invariant set of a flow generated by … with no continuous symmetries other than time-shift invariance. Let…

The diagonal and nondiagonal Bianchi IX models near the cosmological singularity have different topological structures in their spaces of critical points. In both cases these criti…

The Bianchi IX model near the cosmological singularity has diagonal and nondiagonal cases, whose dynamics can be studied through their spaces of critical points. In the diagonal ca…

Generic-distribution conjecture. The distributions reported in Figure are generic in the sense that they qualitatively describe the landing sites associated with each descent mode.

Let $\tau_p$ denote the period of a periodic orbit and let $\tau_{\rm min}$ denote the period of the shortest periodic orbit. The inequality referred to as (Inequality2) has been p…