GBT and Critical Phenomena: Scaling Hypotheses, Critical Exponents, and Universality Classes
摘要
In the previous chapters, we developed the covariant formulation of GBT and applied it to local and global bifurcations in dynamical systems governed by differential equations. In every case studied so far, the scalar curvature diverges at bifurcation points, signaling critical transitions in system behavior. We now seek a unified framework that captures these geometric signatures and connects them to the broader context of critical phenomena.