科研之友
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摘要
We consider the intersections of the complex nodal set N-lambda j(C) of the analytic continuation of an eigenfunction of Delta on a real analytic surface (M-2, g) with the complexification of a geodesic gamma. We prove that if the geodesic flow is ergodic and if gamma is periodic and satisfies a generic asymmetry condition, then the intersection points N-lambda j(C) boolean AND gamma(C)(x,xi) condense along the real geodesic and become uniformly distributed with respect to its arc- length. We prove an analogous result for non-periodic geodesics except that the 'origin'. gamma(x,xi) (0) is allowed to move with lambda(j).
- 出版日期2014-2
- 单位西北大学
