Floquet bundles for scalar parabolic equations

For linear scalar parabolic equations such as on a finite interval 0x, with various boundary conditions, we obtain canonical Floquet solutions u _n (t, x). These solutions are characterized by the property that z(u _n (t, x))=n for all t, where z(·) denotes the zero crossing (lap) number of Matano. The coefficients a(t, x) and b(t, x) are not assumed to be periodic in t, but if they are, the solutions u _n (t, x) reduce to the standard Floquet solutions. Our results may naturally be expressed in the language of linear skew product flows. In this context, we obtain for each N1 an exponential dichotomy between the bundles span {u _n (·,·)} _n ^=1/N and .