Abstract: Transversality
is a powerful technique for proving that some properties on spaces of maps,
solutions of partial differential equations or vector fields are generic. In
particular the properties of the evaluation map constructed to each problem is
the key tool.
In
the setting of dynamical systems given by the pair where
the state space M is a smooth manifold
and is
a continuous map, frequently we have only a partial information of M
throughout a scalar map but
we do not know how is M. As a
consequence, a problem which arises is how to reconstruct M
using a
and getting the essential information on it. The technique of using embeddings
maps is satisfactory since them keep that information. The embedology started
with the works of Whitney in the 1930’s. Since then some results have been
obtained but using different techniques.
In
this paper we present part of those results under the unified approach of the
transversality theory and underlay the importance of the evaluation map
associated to each problem of embedology.
