In mathematics,
Contents
Definition
Two map germs
of the form Ψ(x,y) = (φ(x),ψ(x,y)), satisfying,
In other words, Ψ maps the graph of f to the graph of g, as well as the graph of the zero map to itself. In particular, the diffeomorphism φ maps f−1(0) to g−1(0). The name contact is explained by the fact that this equivalence is measuring the contact between the graph of f and the graph of the zero map.
Contact equivalence is the appropriate equivalence relation for studying the sets of solution of equations, and finds many applications in dynamical systems and bifurcation theory, for example.
It is easy to see that this equivalence relation is weaker than A-equivalence, in that any pair of
KV-equivalence
This modification of