论文标题
双曲线吸引子上的自动伴侣拉普拉斯和对称扩散
Self-adjoint Laplacians and symmetric diffusions on hyperbolic attractors
论文作者
论文摘要
我们在双曲线吸引子上构建了自我伴侣拉普拉斯人和对称的马尔可夫半群，并具有Gibbs $ u $ $ $ - meas。如果该度量得到全部支持，我们还可以得出结论相关的对称扩散过程的存在。在呈负弯曲的歧管上引起的部分双曲线差异的特殊情况下，我们认为的拉普拉斯人是众所周知的经典叶叶laplacians的自我偶像扩展。我们观察到能量密度在$ u $ - 符合案例中的准不转变属性以及零能量的非构函数的存在。
We construct self-adjoint Laplacians and symmetric Markov semigroups on hyperbolic attractors, endowed with Gibbs $u$-measures. If the measure has full support, we can also conclude the existence of an associated symmetric diffusion process. In the special case of partially hyperbolic diffeomorphisms induced by geodesic flows on negatively curved manifolds the Laplacians we consider are self-adjoint extensions of well-known classical leafwise Laplacians. We observe a quasi-invariance property of energy densities in the $u$-conformal case and the existence of nonconstant functions of zero energy.
