Editing Chaos theory (section)

===Infinite dimensional maps===
The straightforward generalization of coupled discrete maps<ref name="Moloney, J V 1986">{{cite journal |title=Solitary waves as fixed points of infinite-dimensional maps for an optical bistable ring cavity: Analysis
|journal=Journal of Mathematical Physics|volume=29 |issue=1 |pages=63 |year=1988
|last1= Adachihara |first1=H
|last2= McLaughlin |first2=D W
|last3= Moloney |first3=J V
|last4= Newell |first4=A C
|doi=10.1063/1.528136 |bibcode=1988JMP....29...63A}}</ref> is based upon convolution integral which mediates interaction between spatially distributed maps:
<math>\psi_{n+1}(\vec r,t)  = \int K(\vec r - \vec r^{,},t) f [\psi_{n}(\vec r^{,},t) ]d {\vec r}^{,}</math>,

where kernel <math>K(\vec r - \vec r^{,},t)</math> is propagator derived as Green function of a relevant physical system,<ref name="Okulov, A Yu 1988">{{cite book |chapter=Spatiotemporal dynamics of a wave packet in nonlinear medium and discrete maps
|title=Proceedings of the Lebedev Physics Institute |language=ru |editor=N.G. Basov |publisher=Nauka |lccn=88174540 |volume=187 |pages=202–222 |year=1988 |last1= Okulov |first1=A Yu |last2=Oraevskiĭ |first2=A N }}</ref>

<math> f [\psi_{n}(\vec r,t) ] </math> might be logistic map alike <math> \psi \rightarrow G \psi [1 - \tanh (\psi)]</math> or [[complex map]]. For examples of complex maps the [[Julia set]] <math> f[\psi] = \psi^2</math> or [[Ikeda map]]
<math> \psi_{n+1} = A + B \psi_n e^{i (|\psi_n|^2 + C)} </math> may serve. When wave propagation problems at distance <math>L=ct</math> with wavelength <math>\lambda=2\pi/k</math> are considered the kernel <math>K</math> may have a form of Green function for [[Schrödinger equation]]:.<ref name="Okulov, A Yu 2000">{{cite journal |title=Spatial soliton laser: geometry and stability
|journal=Optics and Spectroscopy|volume=89 |issue=1 |pages=145–147 |year=2000 |last1= Okulov |first1=A Yu|s2cid=122790937|doi=10.1134/BF03356001  |bibcode=2000OptSp..89..131O}}</ref><ref name="Okulov, A Yu 2020">{{cite journal |title=Structured light entities, chaos and nonlocal maps
|journal=Chaos, Solitons & Fractals|volume=133 |issue=4|page=109638 |year=2020|last1= Okulov |first1=A Yu|doi=10.1016/j.chaos.2020.109638|arxiv=1901.09274|bibcode=2020CSF...13309638O|s2cid=118828500}}</ref>

<math> K(\vec r - \vec r^{,},L)  = \frac {ik\exp[ikL]}{2\pi L}\exp[\frac {ik|\vec r-\vec r^{,}|^2}{2 L} ]</math>.