On Invariant Surfaces And Bifurcation of Periodic Solutions of Ordinary Differen
On Invariant Surfaces And Bifurcation of Periodic Solutions of Ordinary Differen
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■ . We write this as w = a(M)w + e(n)|w|^w + Y«v(s, w, w, m) "♦■ Gif (3. 12) ' h7 - ■where v = a(s, u)v} + b(s, n)\j, a and b vectors. Con- sider the vector differential equation Y + [S'(^) •*■ {Ck-l)a(n) + -ta(^)}I]Y = hCsj^) where prime denotes transpose, I is the identity matrix and h is periodic in s. For n sufficiently small this equation has a unique periodic solution yCs, ^) and the transformation w = C •*■ Y • YCs, ^)C^C'^ (3. 13) carries (3. 12) Into C = aCu)C + pCn)|C|'C + Y • Cv(s, c..., C, m) - hCs, u)c^c^] + Gi, applying this for k = 1, t = 0> h = a(s, ia) and k = 0, -t, = 1, h = t)(s, ij) we obtain the form After carrying out the above transformations on the second equation of (3. 5') we write that equation as Y = S(ia)Y + v(s, C, C»^) + H3 (3. 1^) where v = riCs, n)c^ + ^'zQQ + ^'^V' ^o^ M sufficiently small the vector differential equation Y + CikaCn) + ^, a(^)3I - S(h)]y = h(s, |a) with h periodic in s, has a unique periodic solution yCsj^j. ) and the transformation ^-.
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To quickly assess the difficulty of the text, read a short excerpt:
■ . We write this as w = a(M)w + e(n)|w|^w + Y«v(s, w, w, m) "♦■ Gif (3. 12) ' h7 - ■where v = a(s, u)v} + b(s, n)\j, a and b vectors. Con- sider the vector differential equation Y + [S'(^) •*■ {Ck-l)a(n) + -ta(^)}I]Y = hCsj^) where prime denotes transpose, I is the identity matrix and h is periodic in s. For n sufficiently small this equation has a unique periodic solution yCs, ^) and the transformation w = C •*■ Y • YCs, ^)C^C'^ (3. 13) carries (3. 12) Into C = aCu)C + pCn)|C|'C + Y • Cv(s, c..., C, m) - hCs, u)c^c^] + Gi, applying this for k = 1, t = 0> h = a(s, ia) and k = 0, -t, = 1, h = t)(s, ij) we obtain the form After carrying out the above transformations on the second equation of (3. 5') we write that equation as Y = S(ia)Y + v(s, C, C»^) + H3 (3. 1^) where v = riCs, n)c^ + ^'zQQ + ^'^V' ^o^ M sufficiently small the vector differential equation Y + CikaCn) + ^, a(^)3I - S(h)]y = h(s, |a) with h periodic in s, has a unique periodic solution yCsj^j. ) and the transformation ^-.
What to read after On Invariant Surfaces And Bifurcation of Periodic Solutions of Ordinary Differen?
You can find similar books in the "Read Also" column, or choose other free books by Robert John Sacker to read onlineMoreLess
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