center manifold-07.nb

该程序用来处理微分方程系统的,用来化简一个微分系统的,特别是高维的系统

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    \(\[Omega] = \@\(a\ \((\(-a\) + c)\)\)\), "\n", 
    \(\[Lambda] = \(\(-2\) \(a\)\(\ \)\(c\)\(\ \)\)\/\(a + c\)\), "\n", 
    \(a\_1 = \(\(\@\(a\ \((\(-a\) + c)\)\)\)\(\ \)\(\@\(\(a\ c\ \((\(-a\) + \
c)\)\)\/\(a + c\)\)\)\(\ \)\((a\^4 + 4\ a\^3\ c - 2\ a\^2\ c\^2 + c\^4)\)\(\ \
\)\)\/\(a\ c\ \((a\^4 - 6\ a\^2\ c\^2 + 4\ a\ c\^3 + c\^4)\)\)\), "\n", 
    \(a\_2 = \(\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\)\(\ \)\((a\^4 + \
4\ a\^3\ c - 2\ a\^2\ c\^2 + 2\ a\ c\^3 - c\^4)\)\(\ \)\)\/\(c\ \((a\^4 - 6\ \
a\^2\ c\^2 + 4\ a\ c\^3 + c\^4)\)\)\), "\n", 
    \(a\_3 = \((\@\(a\ \((\(-a\) + c)\)\)\ \@\(\(a\ c\ \((\(-a\) + \
c)\)\)\/\(a + c\)\)\ \((a\^5 + 3\ a\^4\ c - 6\ a\^3\ c\^2 + 8\ a\^2\ c\^3 - 
                3\ a\ c\^4 + c\^5)\)\ )\)/\((a\ c\ \((a\^5 + a\^4\ c - 
                6\ a\^3\ c\^2 - 2\ a\^2\ c\^3 + 5\ a\ c\^4 + 
                c\^5)\))\)\), "\n", 
    \(a\_5\  = \(\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\)\(\ \)\((a\^4 \
+ 4\ a\^3\ c - 2\ a\^2\ c\^2 + 2\ a\ c\^3 - c\^4)\)\(\ \)\)\/\(c\ \((a\^4 - 6\
\ a\^2\ c\^2 + 4\ a\ c\^3 + c\^4)\)\)\), "\n", 
    \(a\_6 = \(-\(\(\(2\)\(\ \)\(\@\(a\ \((\(-a\) + 
                        c)\)\)\)\(\ \)\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + 
                        c\)\)\)\(\ \)\((a\^3 + 4\ a\^2\ c - 5\ a\ c\^2 + 
                  2\ c\^3)\)\(\ \)\)\/\(a\^5 + a\^4\ c - 6\ a\^3\ c\^2 - 
              2\ a\^2\ c\^3 + 5\ a\ c\^4 + 
              c\^5\)\)\)\[IndentingNewLine]\), "\n", 
    \(b\_1\  = \(\(\@\(a\ \((\(-a\) + c)\)\)\)\(\ \)\(\@\(\(a\ c\ \((\(-a\) + \
c)\)\)\/\(a + c\)\)\)\(\ \)\((a\^4 + 4\ a\^3\ c - 2\ a\^2\ c\^2 - 6\ a\ c\^3 \
- c\^4)\)\(\ \)\)\/\(a\ c\ \((a\^4 - 6\ a\^2\ c\^2 + 4\ a\ c\^3 + \
c\^4)\)\)\), "\n", 
    \(b\_2 = \(\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\)\(\ \
\)\((\(-a\^3\) - 5\ a\^2\ c - 3\ a\ c\^2 + c\^3)\)\(\ \)\)\/\(c\ \((\(-a\^3\) \
- a\^2\ c + 5\ a\ c\^2 + c\^3)\)\)\), "\n", 
    \(b\_3 = \((\@\(a\ \((\(-a\) + c)\)\)\ \@\(\(a\ c\ \((\(-a\) + \
c)\)\)\/\(a + c\)\)\ \((a\^5 + 3\ a\^4\ c - 6\ a\^3\ c\^2 - 2\ a\^2\ c\^3 - 
                3\ a\ c\^4 - c\^5)\)\ )\)/\((a\ c\ \((a\^5 + a\^4\ c - 
                6\ a\^3\ c\^2 - 2\ a\^2\ c\^3 + 5\ a\ c\^4 + 
                c\^5)\))\)\), "\n", 
    \(b\_5 = \(\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\)\(\ \
\)\((\(-a\^3\) - 5\ a\^2\ c - 3\ a\ c\^2 + c\^3)\)\(\ \)\)\/\(c\ \((\(-a\^3\) \
- a\^2\ c + 5\ a\ c\^2 + c\^3)\)\)\), "\n", 
    \(b\_6 = \(-\(\(\(2\)\(\ \)\(\@\(a\ \((\(-a\) + 
                        c)\)\)\)\(\ \)\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + 
                        c\)\)\)\(\ \)\((a\^2 + 5\ a\ c + 
                  2\ c\^2)\)\(\ \)\)\/\(a\^4 + 2\ a\^3\ c - 4\ a\^2\ c\^2 - 
              6\ a\ c\^3 - c\^4\)\)\)\), "\n", 
    \(c\_1 = \(\(a\)\(\ \)\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\)\(\ \
\)\(\((a + c)\)\^2\)\(\ \)\)\/\(c\ \((\(-a\^3\) - a\^2\ c + 5\ a\ c\^2 + \
c\^3)\)\)\), "\n", 
    \(c\_2 = \(-\(\(\(\@\(a\ \((\(-a\) + c)\)\)\)\(\ \)\((a + 
                  c)\)\(\ \)\((a\^2 + 
                  c\^2)\)\(\ \)\)\/\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + \
c\)\)\ \((a\^3 + a\^2\ c - 5\ a\ c\^2 - c\^3)\)\)\)\)\), "\n", 
    \(c\_3 = \(\(\((a - c)\)\^2\)\(\ \)\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a \
+ c\)\)\)\(\ \)\((a + c)\)\(\ \)\)\/\(c\ \((\(-a\^3\) - a\^2\ c + 5\ a\ c\^2 \
+ c\^3)\)\)\), "\n", 
    \(c\_5 = \(-\(\(\(\@\(a\ \((\(-a\) + c)\)\)\)\(\ \)\((a + 
                  c)\)\(\ \)\((a\^2 + 
                  c\^2)\)\(\ \)\)\/\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + \
c\)\)\ \((a\^3 + a\^2\ c - 5\ a\ c\^2 - c\^3)\)\)\)\)\), "\n", 
    \(c\_6 = \(\(\@\(\(a\ c\ \((\(-a\) + c)\)\)\/\(a + c\)\)\)\(\ \)\((3\ \
a\^2 + 2\ a\ c - c\^2)\)\(\ \)\)\/\(a\^3 + a\^2\ c - 5\ a\ c\^2 - c\^3\)\), "\
\n", 
    \(d\_1 = \(\[Lambda]\^2\ c\_1 + 2\ \[Omega]\^2\ c\_1 - \[Lambda]\ \
\[Omega]\ c\_2\)\/\(\[Lambda]\ \((\[Lambda]\^2 + 4\ \[Omega]\^2)\)\)\), "\n", \

    \(d\_2 = \(2\ \[Omega]\ c\_1 + \[Lambda]\ c\_2\)\/\(\[Lambda]\^2 + 4\ \
\[Omega]\^2\)\), "\n", 
    \(d\_3 = \(\[Omega]\ \((2\ \[Omega]\ c\_1 + \[Lambda]\ c\_2)\)\)\/\(\
\[Lambda]\ \((\[Lambda]\^2 + 4\ \[Omega]\^2)\)\)\), "\n", 
    \(d\_4 = \(-\(1\/\(\[Lambda]\^7 + 14\ \[Lambda]\^5\ \[Omega]\^2 + 
                49\ \[Lambda]\^3\ \[Omega]\^4 + 
                36\ \[Lambda]\ \[Omega]\^6\)\)\) \((2\ \[Lambda]\^4\ \[Omega]\
\ b\_1\ c\_1 + 10\ \[Lambda]\^2\ \[Omega]\^3\ b\_1\ c\_1 - 
            12\ \[Omega]\^5\ b\_1\ c\_1 - 
            2\ \[Lambda]\^3\ \[Omega]\^2\ b\_2\ c\_1 + 
            2\ \[Lambda]\ \[Omega]\^4\ b\_2\ c\_1 + \[Lambda]\^5\ b\_1\ c\_2 \
+ 5\ \[Lambda]\^3\ \[Omega]\^2\ b\_1\ c\_2 - 
            6\ \[Lambda]\ \[Omega]\^4\ b\_1\ c\_2 - \[Lambda]\^4\ \[Omega]\ b\
\_2\ c\_2 + \[Lambda]\^2\ \[Omega]\^3\ b\_2\ c\_2 - 
            2\ \[Omega]\ a\_2\ \((\((\[Lambda]\^4 + 
                        3\ \[Lambda]\^2\ \[Omega]\^2 + 
                        6\ \[Omega]\^4)\)\ c\_1 - \[Lambda]\ \[Omega]\ \((2\ \
\[Lambda]\^2 + 
                        3\ \[Omega]\^2)\)\ c\_2)\) + \[Lambda]\ a\_1\ \((2\ \
\((\[Lambda]\^4 + 8\ \[Lambda]\^2\ \[Omega]\^2 + 
                        11\ \[Omega]\^4)\)\ c\_1 - \[Lambda]\ \[Omega]\ \((3\ \
\[Lambda]\^2 + 17\ \[Omega]\^2)\)\ c\_2)\) - \[Lambda]\^5\ c\_1\ c\_3 - 
            7\ \[Lambda]\^3\ \[Omega]\^2\ c\_1\ c\_3 - 
            12\ \[Lambda]\ \[Omega]\^4\ c\_1\ c\_3 + 
            2\ \[Lambda]\^4\ \[Omega]\ c\_2\ c\_3 + 
            8\ \[Lambda]\^2\ \[Omega]\^3\ c\_2\ c\_3 + \[Lambda]\^4\ \[Omega]\
\ c\_1\ c\_5 + \[Lambda]\^2\ \[Omega]\^3\ c\_1\ c\_5 + 
            18\ \[Omega]\^5\ c\_1\ c\_5 - 
            3\ \[Lambda]\^3\ \[Omega]\^2\ c\_2\ c\_5 + 
            3\ \[Lambda]\ \[Omega]\^4\ c\_2\ c\_5)\)\), "\n", 
    \(d\_5 = \(1\/\(\[Lambda]\^7 + 14\ \[Lambda]\^5\ \[Omega]\^2 + 
              49\ \[Lambda]\^3\ \[Omega]\^4 + 
              36\ \[Lambda]\ \[Omega]\^6\)\) \((\(-10\)\ \[Lambda]\^3\ \
\[Omega]\^2\ b\_1\ c\_1 - 30\ \[Lambda]\ \[Omega]\^4\ b\_1\ c\_1 - 
            2\ \[Lambda]\^4\ \[Omega]\ b\_2\ c\_1 + 
            2\ \[Lambda]\^2\ \[Omega]\^3\ b\_2\ c\_1 - 
            5\ \[Lambda]\^4\ \[Omega]\ b\_1\ c\_2 - 
            15\ \[Lambda]\^2\ \[Omega]\^3\ b\_1\ c\_2 - \[Lambda]\^5\ b\_2\ c\
\_2 + \[Lambda]\^3\ \[Omega]\^2\ b\_2\ c\_2 - \((\[Lambda]\^2 + 
                  3\ \[Omega]\^2)\)\ a\_1\ \((4\ \((2\ \[Lambda]\^2\ \[Omega] \
+ 3\ \[Omega]\^3)\)\ c\_1 + \[Lambda]\ \((\[Lambda]\^2 - 
                        6\ \[Omega]\^2)\)\ c\_2)\) - 
            2\ \[Lambda]\ a\_2\ \((\((\[Lambda]\^4 + 
                        3\ \[Lambda]\^2\ \[Omega]\^2 + 
                        6\ \[Omega]\^4)\)\ c\_1 - \[Lambda]\ \[Omega]\ \((2\ \
\[Lambda]\^2 + 3\ \[Omega]\^2)\)\ c\_2)\) + 
            5\ \[Lambda]\^4\ \[Omega]\ c\_1\ c\_3 + 
            17\ \[Lambda]\^2\ \[Omega]\^3\ c\_1\ c\_3 + 
            18\ \[Omega]\^5\ c\_1\ c\_3 + \[Lambda]\^5\ c\_2\ c\_3 - 
            2\ \[Lambda]\^3\ \[Omega]\^2\ c\_2\ c\_3 - 
            9\ \[Lambda]\ \[Omega]\^4\ c\_2\ c\_3 + \[Lambda]\^5\ c\_1\ c\_5 \
+ \[Lambda]\^3\ \[Omega]\^2\ c\_1\ c\_5 + 
            18\ \[Lambda]\ \[Omega]\^4\ c\_1\ c\_5 - 
            3\ \[Lambda]\^4\ \[Omega]\ c\_2\ c\_5 + 
            3\ \[Lambda]\^2\ \[Omega]\^3\ c\_2\ c\_5)\)\), "\n", 
    \(d\_6 = \(-\(1\/\(\[Lambda]\^7 + 14\ \[Lambda]\^5\ \[Omega]\^2 + 
                49\ \[Lambda]\^3\ \[Omega]\^4 + 
                36\ \[Lambda]\ \[Omega]\^6\)\)\) \((20\ \[Lambda]\^2\ \
\[Omega]\^3\ b\_1\ c\_1 + 8\ \[Lambda]\^3\ \[Omega]\^2\ b\_2\ c\_1 + 
            12\ \[Lambda]\ \[Omega]\^4\ b\_2\ c\_1 + 
            10\ \[Lambda]\^3\ \[Omega]\^2\ b\_1\ c\_2 + 
            4\ \[Lambda]\^4\ \[Omega]\ b\_2\ c\_2 + 
            6\ \[Lambda]\^2\ \[Omega]\^3\ b\_2\ c\_2 + 
            2\ \[Lambda]\ \[Omega]\ a\_1\ \((4\ \((2\ \[Lambda]\^2\ \[Omega] \
+ 3\ \[Omega]\^3)\)\ c\_1 + \[Lambda]\ \((\[Lambda]\^2 - 
                        6\ \[Omega]\^2)\)\ c\_2)\) + \[Lambda]\^2\ a\_2\ \((2\
\ \((3\ \[Lambda]\^2\ \[Omega] + 
                        7\ \[Omega]\^3)\)\ c\_1 + \[Lambda]\ \((\[Lambda]\^2 \
- \[Omega]\^2)\)\ c\_2)\) - 12\ \[Lambda]\^3\ \[Omega]\^2\ c\_1\ c\_3 - 
            18\ \[Lambda]\ \[Omega]\^4\ c\_1\ c\_3 - 
            3\ \[Lambda]\^4\ \[Omega]\ c\_2\ c\_3 + 
            3\ \[Lambda]\^2\ \[Omega]\^3\ c\_2\ c\_3 - 
            4\ \[Lambda]\^4\ \[Omega]\ c\_1\ c\_5 - 
            4\ \[Lambda]\^2\ \[Omega]\^3\ c\_1\ c\_5 + 
            18\ \[Omega]\^5\ c\_1\ c\_5 - \[Lambda]\^5\ c\_2\ c\_5 + 
            2\ \[Lambda]\^3\ \[Omega]\^2\ c\_2\ c\_5 + 
            9\ \[Lambda]\ \[Omega]\^4\ c\_2\ c\_5)\)\), "\n", 
    \(d\_7 = \(-\(1\/\(\[Lambda]\^7 + 14\ \[Lambda]\^5\ \[Omega]\^2 + 
                49\ \[Lambda]\^3\ \[Omega]\^4 + 
                36\ \[Lambda]\ \[Omega]\^6\)\)\) \((\[Omega]\ \((20\ \
\[Lambda]\ \[Omega]\^3\ b\_1\ c\_1 + 
                8\ \[Lambda]\^2\ \[Omega]\^2\ b\_2\ c\_1 + 
                12\ \[Omega]\^4\ b\_2\ c\_1 + 
                10\ \[Lambda]\^2\ \[Omega]\^2\ b\_1\ c\_2 + 
                4\ \[Lambda]\^3\ \[Omega]\ b\_2\ c\_2 + 
                6\ \[Lambda]\ \[Omega]\^3\ b\_2\ c\_2 + 
                2\ \[Omega]\ a\_1\ \((4\ \((2\ \[Lambda]\^2\ \[Omega] + 
                            3\ \[Omega]\^3)\)\ c\_1 + \[Lambda]\ \((\[Lambda]\
\^2 - 6\ \[Omega]\^2)\)\ c\_2)\) + \[Lambda]\ a\_2\ \((2\ \((3\ \[Lambda]\^2\ \
\[Omega] + 
                            7\ \[Omega]\^3)\)\ c\_1 + \[Lambda]\ \((\[Lambda]\
\^2 - \[Omega]\^2)\)\ c\_2)\) - 12\ \[Lambda]\^2\ \[Omega]\^2\ c\_1\ c\_3 - 
                18\ \[Omega]\^4\ c\_1\ c\_3 - 
                3\ \[Lambda]\^3\ \[Omega]\ c\_2\ c\_3 + 
                3\ \[Lambda]\ \[Omega]\^3\ c\_2\ c\_3 - 
                6\ \[Lambda]\^3\ \[Omega]\ c\_1\ c\_5 -