12 problems

Consider the orbit equations of a perturbed classical relativistic charged particle and dynamical attractors of the type found in the autonomous equation for its off-shell mass dev…

The classical relativistic charged particle is described by nonlinear equations of motion with an autonomous equation for the off-mass-shell deviation, whose phase space appears to…

Tangency-destruction conjecture. This strange attractor is destroyed in the tangency $\mathbf{Tan}_{\Gamma_o}$ between $W^u(\Gamma_o)$ and $W^s(\Gamma_o)$; however, the situation m…

Multifractal-label conjecture. The observed feature reflects the multifractal property of the chaotic system, with each monofractal labelled by $s\in\mathscr{S}$.

Spectral-invariant conjecture. The geometrical and dynamical information of $\mu_{m}$ can be extracted from this spectrum.

Mixed-beta conjecture. The probability density function of $r_{ij}$ can be described by a superposition of incomplete beta distributions,

Let … be H3fnon's two-parameter family of maps on ${\mathbb R}^2$, with the numerical case $(a,b)=(1.4,0.3)$ suggesting a global attractor. H3fnon's conjecture. H3fn conjectured th…

Let $(g_{\boldsymbol{\lambda}})_{\boldsymbol{\lambda}}$ and $(f_{\boldsymbol{\mu}})_{\boldsymbol{\mu}}$ be the two families of dynamical systems considered in the paper. Coordinate…

Let $f_\gamma$ be the one-parameter family of periodically perturbed forced equations … with an attracting heteroclinic network $\Gamma$, and let $\mathcal{F}_\gamma$ be the return…

A kick-generating vector field produces a forcing-shear interaction function as used in the theory of periodically kicked limit cycles. Ott–Stenlund's genericity conjecture. They c…

Consider a generic unfolding of a Hopf-zero singularity, with splitting distances $S^1$ and $S^2$ for the one-dimensional and two-dimensional invariant manifolds, respectively. Let…

Strange-attractor abundance conjecture. For each natural number $n$ there exists an interval $I_n\subset (1/\sqrt{2},t_n)$ such that $\Lambda_t$ displays, at least, $2^{n-1}$ diffe…