7 problems

Let $(g_k^*,f_k^*)$ be the C-type renormalisation two-cycle, and let $R^2$ denote the second iterate of the renormalisation operator. Consider the relevant parts of the spectrum of…

Consider the renormalisation-group dynamics for non-invertible maps with a critical point of continuously varying degree $d$. A C-type two-cycle is a period-two orbit of the renorm…

Let $R$ be the Cvitanović–Feigenbaum operator and let $g^*$ be a nontrivial stationary point satisfying $R(g^*)=g^*$. Restrict attention to the dynamically relevant eigenvalues of…

One-loop AGM RG-flow conjecture. The twist function satisfies

Let $J=J_\rho=\{x\in\mathbb{Z}^2\setminus\{0\}:|x|_\infty\leq\rho\}$ be the standard range-$\rho$ step distribution. Let $\beta_{\operatorname{free}}(J)=8\pi v_J^2$ denote the free…

Let $Q$ be the matrix determining the slope dependence in the two-dimensional critical anisotropic KPZ equation, and let $\mathrm{D}_{\mathrm{bulk}}(t)$ denote its bulk diffusivity…

Let $K_j$, $V_j$, $\bar{V}_j$, $z_j$, and $\mu_j$ be the quantities in the dynamical system and let the error bounds be those in equations (e:VVbar1)--(e:VVbar4), with $j$ the iter…