Modified relative invariants and Liapunov functions

External Stability and Continuous Liapunov Functions

It is well known that external stability of nonlinear input systems can be investigated by means of a suitable extension of the Liapunov functions method. We prove that a complete characterization by means of continuous Liapunov functions is actually possible, provided that the de nition of external stability is appropriately strengthened.

Regularity of Liapunov Functions for Stable Systems

We consider the problem of characterizing those systems which admit (weak) Liapunov functions with nice analytic properties. Our investigation gives a rather complete picture of the situation for the one-dimensional case.

Relative invariants , difference equations , and

Acknowledgements First of all I would like to thank my supervisor Professor T. Kimura. He taught me how to learn mathematics from the beginning when I just started afresh my life. About four years ago he suggested to study on archimedean local zeta functions of several variables as my first research task for the Master's thesis. I can not give enough thanks to his heartwarming encouragement all...

Relative and modified relative realizability

Relative Gromov - Witten invariants

We define relative Gromov-Witten invariants of a symplectic manifold relative to a codimension-two symplectic submanifold. These invariants are the key ingredients in the symplectic sum formula of [IP4]. The main step is the construction of a compact space of ‘V -stable’ maps. Simple special cases include the Hurwitz numbers for algebraic curves and the enumerative invariants of Caporaso and Ha...