ACADSTAFF UGM
| Title | : | On the isometric stochastic flows on exotic spheres ? G M 7 |
| Author | : |
NURFARISHA (1) Dr. Adhitya Ronnie Effendie, S.Si., M.Si., M.Sc. (2) Dr.rer.nat. Muhammad Farchani Rosyid, M.Si. (3) |
| Date | : | 0 2016 |
| Keyword | : | Vector fields, Differential equations, Manifolds, Polynomials, Brownian motion Vector fields, Differential equations, Manifolds, Polynomials, Brownian motion |
| Abstract | : | The possibility of the incompleteness of differentiable vector fields in stochastic differential equations on a manifold related to exotic differential structures is discussed. It is shown that the incompleteness of vector fields due to the chosen differentiable structure (exotica). In this work, the incompleteness of vector fields will be realized from the fact that the isometric stochastic flows in an exotic differential structure are not equivalent to that of (standard) isometric stochastic flows. Isometric stochastic flows with the same one point motion in 7-dimensional standard spheres S7 and 7-dimensional Gromoll-Meyer exotic spheres ?GM7 are studied, these manifolds are homeomorphic but not diffeomorphic. Therefore, the incompleteness of vector fields will have an impact on inequivalence between the isometric stochastic flows on standard sphere S7 and on Gromoll-Meyer sphere ?GM7 in which the isometric stochastic flows is the solution of the stochastic differential equation itself. In this work, isometric stochastic flows on S7 are generated by polynomial quadratic P T(p) which only includes X1, X2, X3, X4, X5, X6, X7, X8, which is called as a right invariant differential operator on G = SO(8). In particular, it will be shown that the dimensions of the space of quadratic polynomials operators which induce zero operators on S7 with SO(8) have dimensions of 70, and SO(8)-isometric stochastic flows with one point motion is a Brownian motion on S7 is represented by a 70-dimensional cube. © 2016 Author(s). |
| Group of Knowledge | : | Matematika |
| Level | : | Internasional |
| Status | : |
Published
|
| No | Title | Action |
|---|---|---|
| 1 |
31_On the Isometric Stochastic Flows on Exotic Spheres.pdf
Document Type : [PAK] Full Dokumen
|
View |