Topological Methods for Ordinary Differential Equations: Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, June 24-July 2, 1991

The volume contains the texts of four courses, given by

the authors at a summer school that sought to present the

state of the art in the growing field of topological methods

in the theory of o.d.e. (in finite and infinitedimension),

and to provide a forum for discussion of the wide variety of

mathematical tools which are involved. The topics covered

range from the extensions of the Lefschetz fixed point and

the fixed point index on ANR's, to the theory of parity of

one-parameter families of Fredholm operators, and from the

theory of coincidence degree for mappings on Banach spaces

to homotopy methods for continuation principles.

CONTENTS: P. Fitzpatrick: The parity as an invariant for

detecting bifurcation of the zeroes of one parameter

families of nonlinear Fredholm maps.- M. Martelli:

Continuation principles and boundary value problems.- J.

Mawhin: Topological degree and boundary value problems for

nonlinear differential equations.- R.D. Nussbaum: The fixed

point index and fixed point theorems.