部分和广义双曲吸引子上的自伴Laplacian
Self-adjoint Laplacians on partially and generalized hyperbolic attractors
摘要：
在部分双曲吸引子和具有奇异性的双曲吸引子上构造了自伴Laplacian算子和对称马尔可夫半群，并赋予Gibbs u-测度.如果该测度是完全支持的，我们也可以保证存在一个相关的对称Hunt扩散过程.在由负截面曲率流形上的测地流诱导的部分双曲型同态的特殊情况下，我们考虑的拉普拉斯算子是著名的经典叶拉普拉斯算子的自伴扩张。
英文摘要：
We construct self-adjoint Laplacians and symmetric Markov semigroups on partially hyperbolic attractors and on hyperbolic attractors with singularities, endowed with Gibbs u-measures. If the measure has full support, we can also guarantee the existence of an associated symmetric Hunt diffusion process. In the special case of partially hyperbolic diffeomorphisms induced by geodesic flows on manifolds of negative sectional curvature the Laplacians we consider are self-adjoint extensions of well-known classical leafwise Laplacians.
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