Connected components of partition preserving diffeomorphisms
Let f:R^2→R be a homogeneous polynomial and S(f) be the group of diffeomorphisms h of R^2 preserving f, i.e. f ° h =f. Denote by S_id (f)^r, (0≤ r ≤ ∞), the identity component of S(f) with respect to the weak Whitney C^r_W-topology. We prove that S_id (f)^∞ = … = S_id (f)^1 for all f and that S_id (f)^1 ot= S_id (f)^0 if and only if f is a product of at least two distinct irreducible over R quadratic forms., number=3, journal=Methods of Functional Analysis and Topology, author=Maksymenko, S., year=2009, month=Sep., pages=264–279