TY  - INPR
A1  - Calin, Ovidium
A1  - Der-Chen, Chang
T1  - The geometry on a step 3 Grushin model
N2  - In this article we study the geometry associated with the sub-elliptic operator ½ (X²1 +X²2), where X1 = ∂x and X2 = x²/2 ∂y are vector fields on R². We show that any point can be connected with the origin by at least one geodesic and we provide an approximate formula for the number of the geodesics between the origin and the points situated outside of the y-axis. We show there are in¯nitely many geodesics between the origin and the points on the y-axis.
T3  - Preprint - (2004) 08 
KW  - Grushin operator
KW  - subRiemannian geometry
KW  - geodesics
KW  - Hamilton-Jacobi theory
KW  - elliptic functions
KW  - Euler's theta functions
Y1  - 2008
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/2471
UR  - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-26724
ER  -