Nusc Messages 752 Reaction score 2 Thread starter Nov 1, 2009 #1 How do I write u''+u*e^x = 0 as a planar system? Last edited: Nov 1, 2009
Nusc Messages 752 Reaction score 2 Nov 2, 2009 #2 Okay its: Let z=u', then z'=u''=-exp(x)*u. So the planar system is {u'=z,z'=-exp(x)*u}, or in matrix form, U'=A*U, where U is the column vector (u,z) and A is the 2x2 matrix (0,1,-exp(x),0). What can be said about the Poincare return map on the transversal u>0?
Okay its: Let z=u', then z'=u''=-exp(x)*u. So the planar system is {u'=z,z'=-exp(x)*u}, or in matrix form, U'=A*U, where U is the column vector (u,z) and A is the 2x2 matrix (0,1,-exp(x),0). What can be said about the Poincare return map on the transversal u>0?