File:Nem0map.jpg

Complex map of the Nemtsov function with parameter $q\!=\!0$:

$u\!+\!\mathrm i v=\mathrm{Nem}_0(x\!+\!\mathrm i y)$

where

$\mathrm{Nem}_0(z)=z+z^3$

C++ generator of map
//using namespace std; typedef std::complex z_type;
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x<y;x++)
 * 1) include
 * 1) define Re(x) x.real
 * 2) define Im(x) x.imag
 * 3) define I z_type(0.,1.)
 * 4) include "conto.cin"

DB Q=0.; z_type nem(z_type z) { return z*(1.+z*z*(1.+z*Q)); }

int main{ int Max; int j,k,m,n; DB x,y, p,q, t,tr,ti; z_type z,c,d;

int M=401,M1=M+1; int N=401,N1=N+1; DB X[M1],Y[N1]; DB *g, *f, *w; // w is working array. g=(DB *)malloc((size_t)((M1*N1)*sizeof(DB))); f=(DB *)malloc((size_t)((M1*N1)*sizeof(DB))); w=(DB *)malloc((size_t)((M1*N1)*sizeof(DB))); char v[M1*N1]; // v is working array //DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array. //char v[M1*N1]; // v is working array

FILE *o;o=fopen("nem0ma.eps","w");ado(o,402,402);

fprintf(o,"201 201 translate\n 100 100 scale 2 setlinecap\n"); DO(m,M1) X[m]=-2.+.01*(m-.5); DO(n,N1) Y[n]=-2.+.01*(n-.5); for(m=-2;m<3;m++){ if(m==0){ M(m,-2.1)L(m,2.1)} else { M(m,-2)L(m,2) }} for(n=-2;n<3;n++){ M(-2,n)L(2,n)} fprintf(o,".006 W 0 0 0 RGB 2 setlinecap S\n");

//M(tr, -2) L(tr, 2) M(-2, ti) L(2, ti) M(-2,-ti) L(2,-ti) fprintf(o,".002 W 0 0 0 RGB S\n");

//M(-2,0) L(0,0) M(tr,ti)L(0,0)L(tr,-ti) //fprintf(o,".01 W 1 1 0 RGB 0 setlinecap S\n");

DO(m,M1)DO(n,N1){g[m*N1+n]=9999999; f[m*N1+n]=9999999;} DO(m,M1){x=X[m]; if(m/10*10==m) printf("run at x=%6.3f\n",x); DO(n,N1){y=Y[n]; z=z_type(x,y);

//c=sunem(z); //c=aun(z); //c=arqnem(z); c=nem(z);

//p=abs(c-z)/abs(c+z); p=-log(p)/log(10.); p=Re(c); q=Im(c); //if(p>-85 && p<85) g[m*N1+n]=p; if(p>-1001 && p<1001 &&        q >-1001 && q<1001 ) { g[m*N1+n]=p; f[m*N1+n]=q; } }}

M(-2,0) L(0,0) M(tr,ti)L(0,0)L(tr,-ti) fprintf(o,".004 W 1 1 0 RGB 0 setlinecap S\n");

fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=20.;q=.5; //#include"plofu.cin" //p=2;q=1;

for(m=-5;m<5;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, (m+.1*n),-q,q); fprintf(o,".002 W 0 .6 0 RGB S\n"); for(m=0;m<5;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q); fprintf(o,".002 W .9 0 0 RGB S\n"); for(m=0;m<5;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q); fprintf(o,".002 W 0 0 .9 RGB S\n");

for(m= 1;m<11;m++) conto(o,f,w,v,X,Y,M,N,(0.-m),-p,p);fprintf(o,".007 W .8 0 0 RGB S\n"); for(m= 1;m<11;m++) conto(o,f,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".007 W 0 0 .8 RGB S\n"); conto(o,f,w,v,X,Y,M,N,(0. ),-p,p);fprintf(o,".007 W .5 0 .5 RGB S\n"); for(m=-10;m<11;m++)conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".007 W 0 0 0 RGB S\n");

/* // conto(o,g,w,v,X,Y,M,N,15.5,-p,p);fprintf(o,".02 W .3 0 .3 RGB S\n"); conto(o,g,w,v,X,Y,M,N,15.,-p,p);fprintf(o,".004 W 0 0 1 RGB S\n"); conto(o,g,w,v,X,Y,M,N,14.,-p,p);fprintf(o,".002 W 0 1 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N,13.,-p,p);fprintf(o,".002 W 1 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N,12.,-p,p);fprintf(o,".004 W 0 0 .7 RGB S\n"); conto(o,g,w,v,X,Y,M,N,11.,-p,p);fprintf(o,".002 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N,10.,-p,p);fprintf(o,".002 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N,9.,-p,p);fprintf(o,".004 W 0 .6 .8 RGB S\n"); conto(o,g,w,v,X,Y,M,N,8.,-p,p);fprintf(o,".002 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N,7.,-p,p);fprintf(o,".002 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N,6.,-p,p);fprintf(o,".004 W 0 .6 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N,5.,-p,p);fprintf(o,".002 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N,4.,-p,p);fprintf(o,".002 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N,3.,-p,p);fprintf(o,".004 W 1 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N,2.,-p,p);fprintf(o,".002 W 0 0 0 RGB S\n"); conto(o,g,w,v,X,Y,M,N,1.,-p,p);fprintf(o,".005 W .5 0 0 RGB S\n");

//M(-2,0) L(0,0) M(tr,ti)L(0,0)L(tr,-ti) //fprintf(o,".011 W 1 1 0 RGB 0 setlinecap S\n");

fprintf(o,"showpage\n%cTrailer",'%'); fclose(o); system("epstopdf nem0ma.eps"); system( "open nem0ma.pdf"); //mac

//getchar; system("killall Preview");// mac

return 0; }

Latex generator of map
%\documentclass[12pt]{article} \documentclass{mcom-l} \usepackage{graphics} \paperwidth 428pt \paperheight 420pt \usepackage{geometry} \usepackage{rotating} \textwidth 1260pt \textheight 1260pt \topmargin -94pt \oddsidemargin -72pt \parindent 0pt \pagestyle{empty} \newcommand \ing {\includegraphics} \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \begin{document} \begin{picture}(424,424) %\put(50,40){\ing{sunem10q10ma6s}} %\put(24,20){\ing{nem120ma}} \put(24,20){\ing{nem0ma}}

\put(11,414){\sx{2}{$y$}} \put(10,316){\sx{2}{$1$}} \put(10,216){\sx{2}{$0$}} \put(-1,116){\sx{2}{$-1$}} \put(-1, 16){\sx{2}{$-2$}} \put( 9, 5){\sx{2}{$-2$}} \put(109, 5){\sx{2}{$-1$}} \put(221, 5){\sx{2}{$0$}} \put(321, 5){\sx{2}{$1$}} \put(416,5){\sx{2}{$x$}} \put(238,273){\sx{2}{\rot{11} $u\!=\!0$\ero}} \put(231,340){\sx{2}{\rot{89} $u\!=\!0$\ero}} \put(76,194){\sx{2}{\rot{89} $u\!=\!-5$\ero}} \put(158,194){\sx{2}{\rot{89} $u\!=\!-1$\ero}} \put(231,200){\sx{2}{\rot{89} $u\!=\!0$\ero}} \put(301,200){\sx{2}{\rot{89} $u\!=\!1$\ero}} \put(333,200){\sx{2}{\rot{89} $u\!=\!2$\ero}} \put(384,200){\sx{2}{\rot{89} $u\!=\!5$\ero}} \put(231, 50){\sx{2}{\rot{89} $u\!=\!0$\ero}} \put(100,125){\sx{2}{\rot{18} $u\!=\!0$\ero}} \put(36,398){\sx{2}{\rot{-0} $u\!=\!10$\ero}} \put(40,371){\sx{2}{\rot{-7} $u\!=\!5$\ero}} \put(370,288){\sx{2}{\rot{-36} $v\!=\!5$\ero}} \put(168,216){\sx{2}{\rot{0} $v\!=\!0$\ero}} \put(362,132){\sx{2}{\rot{39} $v\!=\!-5$\ero}}% \put(146, 64){\sx{2}{\rot{62} $v\!=\!-1$\ero}} \put(160, 64){\sx{2}{\rot{48} $v\!=\!0$\ero}} \put(170, 57){\sx{2}{\rot{32} $v\!=\!1$\ero}}% \put(356, 68){\sx{2}{\rot{-6} $u\!=\!-5$\ero}} \put(357, 32){\sx{2}{\rot{1} $u\!=\!-10$\ero}} \end{picture} \end{document}