Limit cycles of effective theories

Limit cycles in quantum theories.

Renormalization group limit cycles and more chaotic behavior may be commonplace for quantum Hamiltonians requiring renormalization, in contrast to experience based on classical models with critical behavior, where fixed points are far more common. We discuss the simplest quantum model Hamiltonian identified so far that exhibits a renormalization group with both limit cycle and chaotic behavior....

Effective Field Theories in the Large N Limit

Various effective field theories in four dimensions are shown to have exact non-trivial solutions in the limit as the number N of fields of some type becomes large. These include extended versions of the U(N) Gross–Neveu model, the non-linear O(N) σ-model, and the CP model. Although these models are not renormalizable in the usual sense, the infinite number of coupling types allows a complete c...

Limit Cycles of Differential

vol. 37 (2008) No. 1 Book review: LIMIT CYCLES OF DIFFERENTIAL EQUATIONS by Colin Christopher and Chengzhi Li In June 2006 Jaume Llibre and Armengol Gasull organized the Advan ed Course on Limit Cy les and Di erential Equations at the Centre de Re er a Matemàti a in Bar elona. There were three le turers: two by the authors of this book and by Sergey Yakovenko. The book under review ontains the ...

Central and Local Limit Theories in Markov Dependent Random Variables

Identifiability and Limit Cycles

The report discusses when the non-linear dynamic equations of a non-linear system in a limit-cycle can be determined from measured data. The minimal order needed for this turns out to be the minimal dimension in which the stable orbit of the system does not intersect itself. This is illustrated with a fourth order spiking neuron model, which is identified using a non-linear second order differe...