Mathematica for Theoretical Physics by Gerd Baumann : Henonmap

Question

I was following a solved problem from the book mentioned below on the Henon map. However, even after correcting that I still get an error on execution. I am unable to find the exact cause.

Mathematica for Theoretical Physics Classical Mechanics and Nonlinear Dynamics by Gerd Baumann

Here is the code mentioned in the book.

JacobiMatrix[fun_List, vars_List] := Outer[D, fun, vars]
Clear[HenonMap]
HenonMap[{T_, W_}, α_] := 
 Block[{}, {θCos[2πα] - (W - θ^2)
     Sin[2πα], θ*
     Sin[2πα] + (W - θ^2)Cos[2π*α]}]
JacobiMatrix[
  HenonMap[{θ, W}, α], {θ, W}] // MatrixForm
JacobiMatrix[HenonMap[{θ, W}, α], {θ, W}] // 
  Det // Simplify
initial = Table[{i, 0, 0}, {i, 0.1, 0.84, 0.015}];
henonPlot = {};
Do[AppendTo[henonPlot, 
  ListPlot[NestList[HenonMap[#, 0.2114] &, initial[[k]], 255], 
   PlotStyle -> Hue[k/Length[initial]], Frame -> True, 
   AspectRatio -> 1, AxesLabel -> {"θ", "W"}, 
   PlotRange -> {{-1, 1}, {-1, 1}}]], {k, 1, Length[initial]}]

@Ghoster, You are right. There is nothing wrong. I misread it. I've edited my question — user444, Nov 28 '22 at 06:19

score 12 · Accepted Answer · edited Nov 28 '22 at 07:29

12

HenonMap[{T_, W_}, α_] uses T in args but θ in body
initial is 3D, should be 2D

JacobiMatrix[fun_List, vars_List] := Outer[D, fun, vars]
Clear[HenonMap]
HenonMap[{T_, W_}, α_] := 
 Block[{}, {TCos[2πα] - (W - T^2)
     Sin[2πα], T*
     Sin[2πα] + (W - T^2)Cos[2π*α]}]
JacobiMatrix[
  HenonMap[{θ, W}, α], {θ, W}] // MatrixForm
JacobiMatrix[HenonMap[{θ, W}, α], {θ, W}] // 
  Det // Simplify
initial = Table[{i, 0}, {i, 0.1, 0.84, 0.015}];
henonPlot = {};
Do[AppendTo[henonPlot, 
  ListPlot[NestList[HenonMap[#, 0.2114] &, initial[[k]], 255], 
   PlotStyle -> Hue[k/Length[initial]], Frame -> True, 
   AspectRatio -> 1, AxesLabel -> {"θ", "W"}, 
   PlotRange -> {{-1, 1}, {-1, 1}}]], {k, 1, Length[initial]}]
Show[henonPlot]

edited Nov 28 '22 at 07:29

xzczd

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answered Nov 28 '22 at 04:47

I.M.

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Silly me. Thank you for pointing that out – user444 Nov 28 '22 at 04:53
just one more query, Why is that single loop isn't plotting after the Do[...] as shown in book? – user444 Nov 28 '22 at 05:01
1

Do doesn't not return values, in this code plots are appended to a list, you need to use Show to combine them and show. Using Table is more in WM style Show[Table[ListPlot[ ...], {k, 1, Length[initial]}]] – I.M. Nov 28 '22 at 06:06
1

@user84456 That's a compatibility issue, *Plot functions in and before v5 automatically prints the graphic. See this post for more info: https://mathematica.stackexchange.com/a/47123/1871 – xzczd Nov 28 '22 at 07:22
1

@user84456 Which version of Baumann's book are you using? I just checked version 2 of the book, definitions of HenonMap and initial are both correct therein. – xzczd Nov 28 '22 at 07:34

Mathematica for Theoretical Physics by Gerd Baumann : Henonmap

1 Answers1