abstr12

  We prove a generalized version of the Lefschetz fixed point
theorem, and use it to obtain a variety of periodic and aperiodic
solutions for differential delay  equations, in particular, of the
type   x'(t) = f(x(t-1)). Here f :    R --->  R  is
odd and 2-periodic, and we obtain both  strictly periodic
solutions and solutions periodic modulo a multiple of 2. The
qualitative behavior  of  solutions  can be coded by symbol
sequences containing the sequence of levels about which these
solutions oscillate.

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