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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 108867, 3015]*) (*NotebookOutlinePosition[ 109755, 3045]*) (* CellTagsIndexPosition[ 109665, 3039]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Dynamical Systems", "Subtitle"], Cell["\<\ Ivan Cnop Vrije universiteit Brussel icnop@vub.ac.be\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell["Dynamical systems Matrix", "Section"], Cell[CellGroupData[{ Cell["Action of a Matrix", "Subsection"], Cell[BoxData[{ \(\(a = 0.3;\)\), "\n", \(\(b = \(-0.2\);\)\), "\n", \(\(c = 0;\)\), "\n", \(\(d = 0.7;\)\), "\n", \(\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"A", "=", RowBox[{"(", GridBox[{ {"a", "b"}, {"c", "d"} }], ")"}]}]], "Input"], Cell[BoxData[ \({{0.3`, \(-0.2`\)}, {0, 0.7`}}\)], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(A // MatrixForm\)], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0.3`", \(-0.2`\)}, {"0", "0.7`"} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(A // MatrixForm\)], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0.3`", \(-0.2`\)}, {"0", "0.7`"} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(A\ . {x, y} // MatrixForm\)], "Input"], Cell[BoxData[ InterpretationBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(0.3`\ x - 0.2`\ y\)}, {\(0.7`\ y\)} }], "\[NoBreak]", ")"}], MatrixForm[ { Plus[ Times[ 0.29999999999999999, x], Times[ -0.20000000000000001, y]], Times[ 0.69999999999999996, y]}]]], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(Det[A]\)], "Input"], Cell[BoxData[ \(0.21`\)], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(Eigensystem[A]\)], "Input"], Cell[BoxData[ \({{0.7`, 0.3`}, {{\(-0.44721359549995804`\), 0.8944271909999159`}, {1.`, 0.`}}}\)], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(Dot[A, \ A]\)], "Input"], Cell[BoxData[ \({{0.09`, \(-0.19999999999999998`\)}, {0.`, 0.48999999999999994`}}\)], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(A . 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