Fixed Point  From Scholarpedia (Redirected from Fixed points)
Jump to: navigation, search      Fixed point (Mathematics)
The naming convention in Scholarpedia is that fixed points are
for mappings \[x_{n+1} = f(x_n)\] (\(x\) is a fixed point if
\(x=f(x)\)), whereas equilibria are for flows (ODEs) \[x'=f(x)\]
(\(x\) is an equilibrium point if \(f(x)=0\)).      Fixed point
(Quantum and Statistical Field Theory)      In the context of
QSFT, the renormalization group equation for a field theory on a
discretized momentum or position space (e.g. block-spin
transformations), is --mathematically speaking-- a non-linear
functional mapping and the use of the term fixed point is
consistent with the mathematical terminology (as defined above).
Nevertheless, it is widely diffused in QFT community to call
fixed point the equilibrium points of the renormalization group
flow equation for a field theory on a continuous momentum or
position space, that is a non-linear functional flow equation in
terms of a regulator