Plot linear difference equations

Question

How can I plot an unstable node, saddle, and center in linear two-dimensional difference equations? I can plot the stable node, please see the code. Thank you in advance.
Clear[A, pts1, pts2, pts]

A = {{.80, 0}, {0, .64}};

pts1 = Table[NestList[A.# &, {k, 3}, 20], {k, -3, 3}];

pts2 = Table[NestList[A.# &, {k, -3}, 20], {k, -3, 3}];

p1 = ListLinePlot[pts1, PlotStyle -> PointSize[Medium], 
PlotRange -> {{-3.1, 3.1}, {-3.1, 3.1}},

AspectRatio -> Automatic] /.

Line[x_] :> {Arrowheads[{0, 0.04, 0}], Arrow[x]};

p2 = ListLinePlot[pts2, PlotStyle -> PointSize[Medium],

PlotRange -> {{-3.1, 3.1}, {-3.1, 3.1}},

AspectRatio -> Automatic] /.

Line[x_] :> {Arrowheads[{0, 0.04, 0}], Arrow[x]};

Show[p1, p2]

Daniel Huber · Accepted Answer

It is easy to draw this with complex numbers: Exp[I x] will deliver the rotation and f[x] or Exp[f[x]] the distance from the origin.
pts = Table[
    x Exp[I (k + x)], {k, 0, 5}, {x, 0, 
     10, .1}] /. {Complex[a_, b_] -> List[a, b], a_Real -> {a, 0}};
ListLinePlot[pts, PlotStyle -> PointSize[Medium], 
  AspectRatio -> Automatic] /. 
 Line[x_] :> {Arrowheads[{0, 0.04, 0}], Arrow[x]}

Along the same lines we may draw a center:
pts = Table[
    x Exp[I k ], {k, 0, 2 Pi, Pi/5}, {x, 0, 
     10, .1}] /. {Complex[a_, b_] -> List[a, b], a_Real -> {a, 0}};
ListLinePlot[pts, PlotStyle -> PointSize[Medium], 
  AspectRatio -> Automatic] /. 
 Line[x_] :> {Arrowheads[{0, 0.04, 0}], Arrow[x]}

Daniel Huber · Answer

Simply reverse the direction of the arrowhead:
Clear[A, pts1, pts2, pts]

A = {{.80, 0}, {0, .64}};

pts1 = Table[NestList[A.# &, {k, 3}, 20], {k, -3, 3}];

pts2 = Table[NestList[A.# &, {k, -3}, 20], {k, -3, 3}];

p1 = ListLinePlot[pts1, PlotStyle -> PointSize[Medium], 
    PlotRange -> {{-3.1, 3.1}, {-3.1, 3.1}}, 
    AspectRatio -> Automatic] /. 
   Line[x_] :> {Arrowheads[{0, -0.04, 0}], Arrow[x]};

p2 = ListLinePlot[pts2, PlotStyle -> PointSize[Medium], 
    PlotRange -> {{-3.1, 3.1}, {-3.1, 3.1}}, 
    AspectRatio -> Automatic] /. 
   Line[x_] :> {Arrowheads[{0, -0.04, 0}], Arrow[x]};

Show[p1, p2]

Plot linear difference equations

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