27 citations · 201 across the 34 of their papers we have counts for
8 papers · 1 filter
Quantum-Classical Correspondences for Locally Symmetric Spaces
Joachim Hilgert
We review the status of a program, outlined and motivated in the introduction, for the study of correspondences between spectral invariants of partially hyperbolic flows on locally…
Higher rank quantum-classical correspondence
Joachim Hilgert, Tobias Weich, Lasse L. Wolf
For a compact Riemannian locally symmetric space of arbitrary rank we determine the location of certain Ruelle-Taylor resonances for the Weyl chamber action. We p…
Ruelle-Taylor resonances of Anosov actions
Yannick Guedes Bonthonneau, Colin Guillarmou, Joachim Hilgert +1
Combining microlocal methods and a cohomological theory developped by J. Taylor, we define for -Anosov actions a notion of joint Ruelle resonance spectrum. We prove t…
Classical and quantum resonances for hyperbolic surfaces
Colin Guillarmou, Joachim Hilgert, Tobias Weich
For compact and for convex co-compact oriented hyperbolic surfaces, we prove an explicit correspondence between classical Ruelle resonant states and quantum resonant states, except…
Attractor Networks on Complex Flag Manifolds
Joachim Hilgert
Robbin and Salamon showed that attractor-repellor networks and Lyapunov maps are equivalent concepts and illustrate this with the example of linear flows on projective spaces. In t…
Symbolic dynamics for the geodesic flow on locally symmetric orbifolds of rank one
J. Hilgert, A. D. Pohl
We present a strategy for a geometric construction of cross sections for the geodesic flow on locally symmetric orbifolds of rank one. We work it out in detail for ,…