Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Slipantschuk, Julia"'
Building on tools that have been successfully used in the study of rational billiards, such as induced maps and interval exchange transformations, we provide a construction of a one-parameter family of isosceles triangles exhibiting non-periodic traj
Externí odkaz:
http://arxiv.org/abs/2406.17734
Extended dynamic mode decomposition (EDMD) is a data-driven algorithm for approximating spectral data of the Koopman operator associated to a dynamical system, combining a Galerkin method of order N and collocation method of order M. Spectral converg
Externí odkaz:
http://arxiv.org/abs/2404.08512
Autor:
Pollicott, Mark, Slipantschuk, Julia
We present a practical and effective method for rigorously estimating quantities associated to top eigenvalues of transfer operators to very high precision. The method combines explicit error bounds of the Lagrange-Chebyshev approximation with an est
Externí odkaz:
http://arxiv.org/abs/2308.04293
We show that spectral data of the Koopman operator arising from an analytic expanding circle map $\tau$ can be effectively calculated using an EDMD-type algorithm combining a collocation method of order m with a Galerkin method of order n. The main r
Externí odkaz:
http://arxiv.org/abs/2308.01467
Autor:
Pollicott, Mark, Slipantschuk, Julia
Publikováno v:
Math. Comput. Appl. 2023, 28(3), 70
We estabish rigorous estimates for the Hausdorff dimension of the spectra of Laplacians associated to Sierpi\'nski lattices and infinite Sierpi\'nski gaskets and other post-critically finite self-similar sets.
Comment: 20 pages, 6 figures
Comment: 20 pages, 6 figures
Externí odkaz:
http://arxiv.org/abs/2308.00185
A complete description of resonances for rational toral Anosov diffeomorphisms preserving certain Reinhardt domains is presented. As a consequence it is shown that every homotopy class of two-dimensional Anosov diffeomorphisms contains maps with the
Externí odkaz:
http://arxiv.org/abs/2211.05925
Publikováno v:
In Applied and Computational Harmonic Analysis November 2024 73
We show that spectral data of transfer operators given by holomorphic data can be approximated using an effective numerical scheme based on Lagrange interpolation. In particular, we show that for one-dimensional systems satisfying certain complex con
Externí odkaz:
http://arxiv.org/abs/2004.03534
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Extended dynamic mode decomposition (EDMD) provides a class of algorithms to identify patterns and effective degrees of freedom in complex dynamical systems. We show that the modes identified by EDMD correspond to those of compact Perron-Frobenius an
Externí odkaz:
http://arxiv.org/abs/1905.09266