Existence and uniqueness of solutions to Y-systems and TBA equations

Lorenz Hilfiker, Ingo Runkel

We consider Y-system functional equations of the form $$Y_n(x+i)Y_n(x-i)=\prod _{m=1}^N(1+Y_m(x){)}^{G_{nm}}$$ and the corresponding nonlinear integral equations of the Thermodynami…