Katrin FAESSLER

Contact transformations in logarithmic coordinates
Contact form
We write mappings on H 1 as
τ = −e ξ (sin ψ dξ + 3 cos ψ dη).
(ξ, ψ, η) ↦→ (Ξ(ξ, ψ, η), Ψ(ξ, ψ, η), H(ξ, ψ, η))
To define a stretch map fk, 0 < k < 1, set
Ξ(ξ, ψ, η) = kξ.
Then the contact condition yields
H(ξ, ψ, η) = H(ξ, η), Ψ(ξ, ψ, η) = tan −1
Hη(ξ, η) tan ψ − 3Hξ(ξ, η)
.
k
The stretch map is obtained by setting
H(ξ, η) = η.
Katrin Fässler (University of Helsinki) A stretch map on H 1
HCAA 2012 11 / 23