SetDirectory["~/Dropbox/jakies-rzeczy-moje/Biblioteczka/SL2R/"];

1 parameter groups in SL(2,R)

(0,1,0) direction

origin= Graphics[{PointSize[Large],Black,Point[{0.0,0.0}]}];
saxis= Graphics[{Thick,Arrowheads[Large],Arrow[{{-3,0},{3,0}}]}];
identitysymbol="𝕝";
identitytext=Graphics[{Text["𝕝",{0.0,-0.35},BaseStyle->{FontSize->14}],
Text["0",{0.0,0.35},BaseStyle->{FontSize->14}]}];
saxislabel=Graphics[{Text["exp((Subscript[sσ, 1]))",{3.1,-0.5},BaseStyle->{FontSize->14}],
Text["s",{2.8,0.35},BaseStyle->{FontSize->14}]}];
sExpExample=Graphics[{Text[(1/2)MatrixForm[{{"x+(1/x)","x-(1/x)"},{"x-(1/x)","x+(1/x)"}}],{1.4,-0.7}],
Text["ln(x)",{1.4,0.35},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{1.4,0.0}]},
Text[(1/2)MatrixForm[{{"x+(1/x)","(1/x)-x"},{"(1/x)-x","x+(1/x)"}}],{-1.4,-0.7}],
Text["-ln(x)",{-1.4,0.35},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{-1.4,0.0}]}}];
Show[saxis,origin,identitytext,saxislabel]

Export["saxis.eps",%];

Show[saxis,origin,identitytext,saxislabel,sExpExample]

Export["saxis1.eps",%];

(1,0,0) direction

taxis= Graphics[{
Thick,Arrowheads[Large],Arrow[{{0,-0.1},{0,1}}],
Text["exp((Subscript[tiσ, 2]))",{-0.14,0.95},BaseStyle->{FontSize->14}],
Text["t",{0.04,0.95},BaseStyle->{FontSize->14}]
}];
torigin= Graphics[{
PointSize[Large],Black,Point[{0.0,0.0}],
Text["𝕝",{-0.05,0.0},BaseStyle->{FontSize->14}],
Text["0",{0.05,0.0},BaseStyle->{FontSize->14}]
}];
tExpExample=Graphics[{
Text["(Subscript[iσ, 2])",{-0.25,0.55},BaseStyle->{FontSize->14}],
Text["(π/2)",{0.5,0.5},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,0.5}]}
}];
Show[taxis,torigin]

Export["taxis.eps",%];

taxis= Graphics[{
Thick,Arrowheads[Large],Arrow[{{0,-3},{0,3}}],
Text["exp((Subscript[tiσ, 2]))",{-0.7,2.75},BaseStyle->{FontSize->14}],
Text["t",{0.25,2.75},BaseStyle->{FontSize->14}]
}];
torigin= Graphics[{
PointSize[Large],Black,Point[{0.0,0.0}],
Text["𝕝",{-0.35,0.0},BaseStyle->{FontSize->14}],
Text["0",{0.35,0.0},BaseStyle->{FontSize->14}]
}];
Show[taxis,torigin,tExpExample]

Export["taxis1.eps",%];

tExpExample2=Graphics[{
Text["-𝕝",{-0.25,1},BaseStyle->{FontSize->14}],
Text["π",{0.5,1},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,1}]},
Text["-𝕝",{-0.25,-1},BaseStyle->{FontSize->14}],
Text["-π",{0.5,-1},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,-1}]},
Text["𝕝",{-0.25,-2},BaseStyle->{FontSize->14}],
Text["-2π",{0.5,-2},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,-2}]},
Text["𝕝",{-0.25,2},BaseStyle->{FontSize->14}],
Text["2π",{0.5,2},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,2}]}
}];
Show[taxis,torigin,tExpExample,tExpExample2]

Export["taxis2.eps",%];

((1/2),(1/2),0) dierction

taxis= Graphics[{
Thick,Arrowheads[Large],Arrow[{{0,-3},{0,3}}],
Text["exp((Subscript[tiσ, 2]))",{-0.9,2.75},BaseStyle->{FontSize->14}],
Text["t",{0.3,2.8},BaseStyle->{FontSize->14}]
}];
tExpExample2=Graphics[{
Text["-𝕝",{-0.25,1},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,1}]},
Text["-𝕝",{-0.25,-1},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,-1}]},
Text["𝕝",{-0.25,-2},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,-2}]},
Text["𝕝",{-0.25,2},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,2}]}
}];
dExpExample=Graphics[{
Text["𝕝+(SubPlus[τA])",{1,1}+{0.4,0.3},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{1,1}]},
Text["(2^(Subscript[σ, 1]))",{(Sqrt[2])*Log[2]+0.19,-0.3},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{(Sqrt[2])*Log[2],0.0}]}
}];
Show[taxis,tExpExample2,saxis,saxislabel,dExpExample]

Export["daxis.eps",%];

dExpExample1=Graphics[{
Text["𝕝+(SubMinus[A])",{1,-1}-{-0.4,0.3},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{1,-1}]},
Text["(2^(Subscript[σ, 1]))",{(Sqrt[2])*Log[2]+0.19,-0.3},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{(Sqrt[2])*Log[2],0.0}]}
}];
dExpExample=Graphics[{
Text["𝕝+(SubPlus[A])",{1,1}+{0.4,0.3},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{1,1}]}
}];
Show[taxis,tExpExample2,saxis,saxislabel,dExpExample,dExpExample1]

Export["daxis2.eps",%];

dExpExample2=Graphics[{
Dashed,Line[{{-3,-3},{3,3}}],
Line[{{-3,3},{3,-3}}]
}];
Show[taxis,tExpExample2,saxis,saxislabel,dExpExample,dExpExample1,dExpExample2]

Export["daxis3.eps",%];

θ=((1.6π)/4);
dPeriodicLine=Graphics[{
Line[{{3*Cos[θ+π],3*Sin[θ+π]},{3*Cos[θ],3*Sin[θ]}}]
}];
dHyperbola0=Plot[((Sqrt[(((x*π(Sqrt[2])))^2)+2*(((π))^2)])/(π(Sqrt[2]))),{x,-3,3},PlotRange->{-3,3},PlotStyle->Black];
Show[taxis,tExpExample2,saxis,saxislabel,dExpExample,dExpExample1,dExpExample2,dPeriodicLine]

Export["daxis4.eps",%];

dPeriodicLine=Graphics[{
Line[{{3*Cos[θ+π],3*Sin[θ+π]},{3*Cos[θ],3*Sin[θ]}}],
{PointSize[Large],Black,Point[{(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}]},
Text["-𝕝",{(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}+{-0.1,0.2},BaseStyle->{FontSize->14}]
}];
Show[taxis,tExpExample2,saxis,saxislabel,dExpExample,dExpExample1,dExpExample2,dPeriodicLine]

Export["daxis5.eps",%];

dPeriodicLine=Graphics[{
Line[{{3*Cos[θ+π],3*Sin[θ+π]},{3*Cos[θ],3*Sin[θ]}}],
{PointSize[Large],Black,Point[{(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}]},
Text["-𝕝",{(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}+{-0.1,0.2},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{(2/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(2/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}]},
Text["𝕝",{(2/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(2/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}+{-0.1,0.2},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{((-2)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],((-2)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}]},
Text["𝕝",{((-2)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],((-2)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}-{-0.05,0.25},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{((-1)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],((-1)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}]},
Text["-𝕝",{((-1)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],((-1)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}-{-0,0.25},BaseStyle->{FontSize->14}],
}];
Show[taxis,tExpExample2,saxis,saxislabel,dExpExample,dExpExample1,dExpExample2,dPeriodicLine]

Export["daxis6.eps",%];

dHyperbola0=Plot[((Sqrt[(((x*π(Sqrt[2])))^2)+2*(((π))^2)])/(π(Sqrt[2]))),{x,-3,3},PlotRange->{-3,3},PlotStyle->Black];
dHyperbolatxt=Graphics[{
Text["-𝕝",{(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}+{-0.1,0.2},BaseStyle->{FontSize->14}]
}];
Show[taxis,tExpExample2,saxis,saxislabel,dExpExample,dExpExample1,dExpExample2,dHyperbola0]

Export["daxis7.eps",%];

dHyperbola0=Plot[((Sqrt[(((x*π(Sqrt[2])))^2)+2*(((π))^2)])/(π(Sqrt[2]))),{x,-3,3},PlotRange->{-3,3},PlotStyle->Black];
dHyperbola1=Plot[((Sqrt[(((x*π(Sqrt[2])))^2)+2*(((2*π))^2)])/(π(Sqrt[2]))),{x,-3,3},PlotRange->{-3,3},PlotStyle->Black];
dHyperbolam0=Plot[-((Sqrt[(((x*π(Sqrt[2])))^2)+2*(((π))^2)])/(π(Sqrt[2]))),{x,-3,3},PlotRange->{-3,3},PlotStyle->Black];
dHyperbolam1=Plot[-((Sqrt[(((x*π(Sqrt[2])))^2)+2*(((2*π))^2)])/(π(Sqrt[2]))),{x,-3,3},PlotRange->{-3,3},PlotStyle->Black];

dHyperbolatxt=Graphics[{
Text["-𝕝",{(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}+{-0.1,0.2},BaseStyle->{FontSize->14}]
}];
Show[taxis,tExpExample2,saxis,saxislabel,dExpExample,dExpExample1,dExpExample2,dHyperbola0,dHyperbola1,dHyperbolam0,dHyperbolam1]

Export["daxis8.eps",%];

Artistic vision

taxis= Graphics[{
Thick,Arrowheads[Large],Arrow[{{0,-3},{0,3}}]
}];
dPeriodicLine=Graphics[{
{Thick,Orange,Line[{{3*Cos[θ+π],3*Sin[θ+π]},{3*Cos[θ],3*Sin[θ]}}]},
{PointSize[Large],Black,Point[{(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}]},
Text["-𝕝",{(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}+{-0.1,0.2},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{((-1)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],((-1)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}]},
Text["-𝕝",{((-1)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],((-1)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}-{-0,0.25},BaseStyle->{FontSize->14}],
PointSize[Large],Black,Point[{(2/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(2/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}],
Text["𝕝",{(2/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(2/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}+{-0.1,0.2},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{((-2)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],((-2)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}]},
Text["𝕝",{((-2)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],((-2)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}-{-0,0.25},BaseStyle->{FontSize->14}]
}];
dHyperbola0=Plot[((Sqrt[(((x*π(Sqrt[2])))^2)+2*(((π))^2)])/(π(Sqrt[2]))),{x,-3,3},PlotRange->{-3,3},PlotStyle->Black];
dHyperbola1=Plot[((Sqrt[(((x*π(Sqrt[2])))^2)+2*(((2*π))^2)])/(π(Sqrt[2]))),{x,-3,3},PlotRange->{-3,3},PlotStyle->Black];
dHyperbolam0=Plot[-((Sqrt[(((x*π(Sqrt[2])))^2)+2*(((π))^2)])/(π(Sqrt[2]))),{x,-3,3},PlotRange->{-3,3},PlotStyle->Black];
dHyperbolam1=Plot[-((Sqrt[(((x*π(Sqrt[2])))^2)+2*(((2*π))^2)])/(π(Sqrt[2]))),{x,-3,3},PlotRange->{-3,3},PlotStyle->Black];

dHyperbolatxt=Graphics[{
Text["-𝕝",{(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}+{-0.1,0.2},BaseStyle->{FontSize->14}]
}];
Show[dExpExample2,dHyperbola0,dHyperbola1,dHyperbolam0,dHyperbolam1,dPeriodicLine]

Export["art0.eps",%];

taxis= Graphics[{
Thick,Arrowheads[Large],Arrow[{{0,-3},{0,3}}]
}];

dHyperbolatxt=Graphics[{
Text["-𝕝",{(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}+{-0.1,0.2},BaseStyle->{FontSize->14}]
}];
dPeriodicLine=Graphics[{
{Thick,Orange,Line[{{3*Cos[θ+π],3*Sin[θ+π]},{3*Cos[θ],3*Sin[θ]}}]},
{PointSize[Large],Black,Point[{(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}]},
Text["-𝕝",{(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],(1/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}+{-0.1,0.2},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{((-1)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],((-1)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}]},
Text["-𝕝",{((-1)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Cos[θ],((-1)/(Sqrt[-((Cos[θ])^2)+((Sin[θ])^2)]))*Sin[θ]}-{-0,0.25},BaseStyle->{FontSize->14}]
}];
identitytext=Graphics[{Text["𝕝",{0.0,-0.35},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,0.0}]}}];

Show[identitytext,dExpExample2,dHyperbola0,dHyperbolam0,dPeriodicLine]

Export["art1.eps",%];

dPeriodicLine=Graphics[{
Line[{{3*Cos[θ+π],3*Sin[θ+π]},{3*Cos[θ],3*Sin[θ]}}]
}];
e0=Plot[(1-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
me0=Plot[-(1-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
e1=Plot[2-(1-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
me1=Plot[-2+(1-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
identitytext=Graphics[{Text["𝕝",{0.0,-0.35},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,0.0}]}}];
dPeriodicLine=ParametricPlot[{0.8*((Sin[t])^2)*(t/(Abs[t])),((2*t)/π)},{t,-π,π},PlotStyle->{Orange}];
mOnes=Graphics[{
{PointSize[Large],Black,Point[{0.0,2.0}]},
Text["-𝕝",{0.0,2.0}+{-0.1,0.2},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,-2.0}]},
Text["-𝕝",{0.0,-2.0}-{-0,0.25},BaseStyle->{FontSize->14}]
}];

Show[identitytext,dPeriodicLine,e0,me0,e1,me1,mOnes]

Export["art2.eps",%];

parabolicLine=Plot[(1-Exp[-Abs[x]])*(x/(Abs[x])),{x,-3,3},PlotStyle->{Red}];
Show[identitytext,dPeriodicLine,e0,me0,e1,me1,mOnes,parabolicLine]

Export["art3.eps",%];

hyperbolicLine=Plot[0.6*(1-Exp[-Abs[x]])*(x/(Abs[x])),{x,-3,3},PlotStyle->{}];
Show[identitytext,dPeriodicLine,e0,me0,e1,me1,mOnes,parabolicLine,hyperbolicLine]

Export["art4.eps",%];

The whole surrounding of the SL(2,R)

eLL=RegionPlot[
{y>(1-Exp[-Abs[x]])&&y<2-(1-Exp[-Abs[x]])||
y>-2+(1-Exp[-Abs[x]])&&y<-(1-Exp[-Abs[x]])},
{x,-4,4},{y,-3,3},
BoundaryStyle->None,
PlotStyle->];
Show[identitytext,eLL,identitytext,e0,me0,e1,me1,mOnes]

Export["1otoczEll.eps",%];

pAR=Plot[{(1-Exp[-Abs[x]])*(x/(Abs[x])),-(1-Exp[-Abs[x]])*(x/(Abs[x]))},{x,-3,3},PlotStyle->{Red,Red}];
Show[identitytext,eLL,e1,me1,pAR,mOnes,identitytext]

Export["1otoczEllPar.eps",%];

hYP=RegionPlot[{y<(1-Exp[-Abs[x]])&&y>-(1-Exp[-Abs[x]])},{x,-3,3},{y,-3,3},BoundaryStyle->None,PlotStyle->];
Show[identitytext,eLL,e1,me1,hYP,pAR,mOnes,identitytext]

Export["1otoczEllParHyp.eps",%];

mOnes=Graphics[{
{PointSize[Large],Black,Point[{0.0,2.0}]},
Text["𝕝",{0.0,2.0}+{-0.1,0.2},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,-2.0}]},
Text["𝕝",{0.0,-2.0}-{-0,0.25},BaseStyle->{FontSize->14}]
}];
identitytext=Graphics[{Text["-𝕝",{0.0,-0.35},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,0.0}]}}];
hYPm=RegionPlot[{y<-2+(1-Exp[-Abs[x]])||y>2-(1-Exp[-Abs[x]])},{x,-3,3},{y,-2,2},BoundaryStyle->None,PlotStyle->];
pARm=Plot[{-2+(1-Exp[-Abs[x]]),2-(1-Exp[-Abs[x]])},{x,-3,3},PlotStyle->{{Thick,Blue},{Thick,Blue}}];
Show[identitytext,eLL,e0,me0,hYPm,pARm,mOnes,identitytext]

Export["m1otoczEllParHyp.eps",%];

Universal covering

dPeriodicLine=Graphics[{
Line[{{3*Cos[θ+π],3*Sin[θ+π]},{3*Cos[θ],3*Sin[θ]}}]
}];
e0=Plot[(1-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
me0=Plot[-(1-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
e1=Plot[2-(1-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
me1=Plot[-2+(1-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
identitytext=Graphics[{Text["𝕝",{0.3,0.0},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,0.0}]}}];
dPeriodicLine=ParametricPlot[{0.8*((Sin[t])^2)*(t/(Abs[t])),((2*t)/π)},{t,-π,π},PlotStyle->{Orange}];
mOnes=Graphics[{
{PointSize[Large],Black,Point[{0.0,2.0}]},
Text["-𝕝",{0.0,2.0}+{-0.1,0.2},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,-2.0}]},
Text["-𝕝",{0.0,-2.0}-{-0,0.25},BaseStyle->{FontSize->14}]
}];

Show[identitytext,dPeriodicLine,e0,me0,e1,me1,mOnes]

Export["cover0.eps",%];

dPeriodicLine=Graphics[{
Line[{{3*Cos[θ+π],3*Sin[θ+π]},{3*Cos[θ],3*Sin[θ]}}]
}];
e0=Plot[(1-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
me0=Plot[-(1-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
e1=Plot[2-(1-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
me1=Plot[-2+(1-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
identitytext=Graphics[{Text["𝕝",{0.0,-0.35},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,0.0}]}}];
dPeriodicLine=ParametricPlot[{0.8*((Sin[t])^2)*(t/(Abs[t])),((2*t)/π)},{t,-π,π},PlotStyle->{Orange}];
mOnes=Graphics[{
{PointSize[Large],Black,Point[{0.0,2.0}]},
Text["(Subscript[𝕝, 1])",{0.0,2.0}+{+0.3,0.0},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,-2.0}]},
Text["(Subscript[𝕝, -1])",{0.0,-2.0}+{0.3,0.0},BaseStyle->{FontSize->14}]
}];
identitytext=Graphics[{Text["(Subscript[𝕝, 0])",{0.3,0.0},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,0.0}]}}];
Show[identitytext,dPeriodicLine,e0,me0,e1,me1,mOnes]

Export["cover1.eps",%];

dPeriodicLine=Graphics[{
Line[{{3*Cos[θ+π],3*Sin[θ+π]},{3*Cos[θ],3*Sin[θ]}}]
}];
e2=Plot[(3-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
me3=Plot[4-(1-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
e3=Plot[(5-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
me4=Plot[6-(1-Exp[-Abs[x]]),{x,-3,3},PlotStyle->{Dashed,Black}];
dPeriodicLine=ParametricPlot[{0.8*((Sin[t])^2)*((Sin[t])/(Abs[Sin[t]])),((2*t)/π)},{t,-π,3*π},PlotStyle->{Orange}];
mOnes2=Graphics[{
{PointSize[Large],Black,Point[{0.0,4.0}]},
Text["(Subscript[𝕝, 2])",{0.0,4.0}+{0.3,0.0},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,6.0}]},
Text["(Subscript[𝕝, 3])",{0.0,6.0}+{0.3,0.0},BaseStyle->{FontSize->14}]
}];
Show[identitytext,dPeriodicLine,e0,me0,e1,e2,e3,me3,me4,me1,mOnes,mOnes2]

Export["cover2.eps",%];

eLLCover=RegionPlot[
{y>(1-Exp[-Abs[x]])&&y<2-(1-Exp[-Abs[x]])||
y>2+(1-Exp[-Abs[x]])&&y<4-(1-Exp[-Abs[x]])||
y>4+(1-Exp[-Abs[x]])&&y<6-(1-Exp[-Abs[x]])||
y>-2+(1-Exp[-Abs[x]])&&y<-(1-Exp[-Abs[x]])
},
{x,-5,5},{y,-3,8},
BoundaryStyle->None,
PlotStyle->];
Show[identitytext,eLLCover,e0,me0,e1,e2,e3,me3,me4,me1,mOnes,mOnes2,identitytext]

Export["cover3.eps",%];

Show[identitytext,eLLCover,pAR,e1,e2,e3,me3,me4,me1,mOnes,mOnes2,identitytext]

Export["cover4.eps",%];

Show[identitytext,eLLCover,hYP,pAR,e1,e2,e3,me3,me4,me1,mOnes,mOnes2,identitytext]

Export["cover5.eps",%];

identitytext=Graphics[{Text["(Subscript[𝕝, 0])",{0.3,0.0},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,0.0}]}}];
mOnes=Graphics[{
{PointSize[Large],Black,Point[{0.0,2.0}]},
Text["(Subscript[𝕝, 1])",{0.0,2.0}+{+0.3,0.0},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,-2.0}]},
Text["(Subscript[𝕝, -1])",{0.0,-2.0}+{0.3,0.0},BaseStyle->{FontSize->14}]
}];
mOnes2=Graphics[{
{PointSize[Large],Black,Point[{0.0,4.0}]},
Text["(Subscript[𝕝, 2])",{0.0,4.0}+{0.3,0.0},BaseStyle->{FontSize->14}],
{PointSize[Large],Black,Point[{0.0,6.0}]},
Text["(Subscript[𝕝, 3])",{0.0,6.0}+{0.3,0.0},BaseStyle->{FontSize->14}]
}];
hYPm=RegionPlot[{y<2+(1-Exp[-Abs[x]])&&y>2-(1-Exp[-Abs[x]])},{x,-3,3},{y,-3,3},BoundaryStyle->None,PlotStyle->];
pARm=Plot[{2+(1-Exp[-Abs[x]])*(x/(Abs[x])),2-(1-Exp[-Abs[x]])*(x/(Abs[x]))},{x,-3,3},PlotStyle->{{Thick,Blue},{Thick,Blue}}];
Show[identitytext,eLLCover,e0,hYPm,pARm,e3,me3,me4,me0,me1,mOnes,mOnes2,identitytext]

Export["cover6.eps",%];