A={{2,1},{0,1}}

K={{k1,k2}}

B={0,1}

A-{{0,0},{K1,K2}}

Det[A-{{0,0},{K1,K2}}-{{s,0},{0,s}}]

Expand[(s+3)(s+2)]

AA={{7,0,1},{1,8,-1},{-9,-9,0}}

Det[AA]

Clear[f]
f[0]:=0.5(1+Sqrt[5])+.05
f[t_]:=f[t-1]^2-1
ListPlot[Table[f[t],{t,0,5}],Filling->Axis,PlotRange->{{0,5.1},{0,20}},PlotMarkers->{Automatic,10}]

e[0]:=0.5(1+Sqrt[5])+.05
e[t_]:=0.5(1+Sqrt[5])+.05(1+Sqrt[5])^t
ListPlot[{Table[f[t],{t,0,5}],Table[e[t],{t,0,5}]},Filling->Axis,PlotRange->{{0,5.1},{0,20}},PlotMarkers->{Automatic,10}]

Clear[f]
f[0]:=-1
f[t_]:=f[t-1]^2-1
ListPlot[Table[f[t],{t,0,5}],Filling->Axis,PlotRange->All,PlotMarkers->{Automatic,10}]

Table[f[t],{t,0,5}]

Clear[f]
f[0]:=0
f[t_]:=f[t-1]^2-1
ListPlot[Table[f[t],{t,0,5}],Filling->Axis,PlotRange->All,PlotMarkers->{Automatic,10}]

Clear[f]
f[0]:=0.5(.9+Sqrt[5])
f[t_]:=f[t-1]^2-1
ListPlot[Table[f[t],{t,0,20}],Filling->Axis,PlotRange->All,PlotMarkers->{Automatic,10}]

Clear[f]
f[0]:=-0.5(.9+Sqrt[5])
f[t_]:=f[t-1]^2-1
ListPlot[Table[f[t],{t,0,20}],Filling->Axis,PlotRange->All,PlotMarkers->{Automatic,10}]

Clear[f]
f[0]:=0.5(1-Sqrt[5])
f[t_]:=f[t-1]^2-1
ListPlot[Table[f[t],{t,0,20}],Filling->Axis,PlotRange->All,PlotMarkers->{Automatic,10}]

Clear[f]
f[0]:=0.5(1+Sqrt[5])
f[t_]:=f[t-1]^2-1
ListPlot[Table[f[t],{t,0,20}],Filling->Axis,PlotRange->All,PlotMarkers->{Automatic,10}]

Clear[f,e]
f[0,e_]:=0.5(1+Sqrt[5])-e
f[t_,e_]:=f[t-1,e]^2-1
Manipulate[ListPlot[Table[f[t,e],{t,0,20}],Filling->Axis,PlotRange->All,PlotMarkers->{Automatic,10}],{e,0,(1+Sqrt[5])}]

(.5+.5Sqrt[5])^2+1

.5(5+Sqrt[5])

0.5(1+Sqrt[5])

2 1.618033988749895`

Expand[((x0+eps)^2-1)^2-1]

Expand[(((x0+eps)^2-1)^2-1)^2-1]

Expand[((((x0+eps)^2-1)^2-1)^2-1)^2-1]

Clear[f,e]
f[0,e_]:=e
f[t_,e_]:=f[t-1,e]^2-7/4
Manipulate[ListPlot[Table[f[t,e],{t,0,100}],Filling->Axis,PlotRange->All,PlotMarkers->{Automatic,10}],{e,-1.9,1.9}]

Clear[f,e]
f[0,e_]:=e
f[t_,e_]:=f[t-1,e]^2-2
Manipulate[ListPlot[Table[f[t,e],{t,0,75}],Filling->Axis,PlotRange->All,PlotMarkers->{Automatic,10}],{e,-2,2}]