@article{FroylandKoltaiStahn2020,
  author    = {Froyland, Gary and Koltai, Peter and Stahn, Martin},
  title     = {Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration},
  series = {SIAM journal on applied dynamical systems},
  volume    = {19},
  journal   = {SIAM journal on applied dynamical systems},
  number    = {3},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {1536-0040},
  doi       = {10.1137/19M1261791},
  pages     = {1659 -- 1700},
  year      = {2020},
  abstract  = {Understanding the macroscopic behavior of dynamical systems is an important tool to unravel transport mechanisms in complex flows. A decomposition of the state space into coherent sets is a popular way to reveal this essential macroscopic evolution. To compute coherent sets from an aperiodic time-dependent dynamical system we consider the relevant transfer operators and their infinitesimal generators on an augmented space-time manifold. This space-time generator approach avoids trajectory integration and creates a convenient linearization of the aperiodic evolution. This linearization can be further exploited to create a simple and effective spectral optimization methodology for diminishing or enhancing coherence. We obtain explicit solutions for these optimization problems using Lagrange multipliers and illustrate this technique by increasing and decreasing mixing of spatial regions through small velocity field perturbations.},
  language  = {en}
}
@article{KoltaiLiePlonka2019,
  author    = {Koltai, Peter and Lie, Han Cheng and Plonka, Martin},
  title     = {Frechet differentiable drift dependence of Perron-Frobenius and Koopman operators for non-deterministic dynamics},
  series = {Nonlinearity},
  volume    = {32},
  journal   = {Nonlinearity},
  number    = {11},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {0951-7715},
  doi       = {10.1088/1361-6544/ab1f2a},
  pages     = {4232 -- 4257},
  year      = {2019},
  abstract  = {We prove the Fr{\´e}chet differentiability with respect to the drift of Perron-Frobenius and Koopman operators associated to time-inhomogeneous ordinary stochastic differential equations. This result relies on a similar differentiability result for pathwise expectations of path functionals of the solution of the stochastic differential equation, which we establish using Girsanov's formula. We demonstrate the significance of our result in the context of dynamical systems and operator theory, by proving continuously differentiable drift dependence of the simple eigen- and singular values and the corresponding eigen- and singular functions of the stochastic Perron-Frobenius and Koopman operators.},
  language  = {en}
}