A tale of two vortices: How numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems [PDF]
Journal of Computational Dynamics, 2020 Coherent structures are spatially varying regions which disperse minimally over time and organise motion in non-autonomous systems. This work develops and implements algorithms providing multilayered descriptions of time-dependent systems which are not only useful for locating coherent structures, but also for detecting time windows within which these ...
Blachut, Chantelle +1 more
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Ergodic Theory and Dynamical Systems [PDF]
, 2013 This is the proceedings of the workshop on recent developments in ergodic theory and dynamical systems on March 2011 and March 2012 at the University of North Carolina at Chapel Hill. The articles in this volume cover several aspects of vibrant research in ergodic theory and dynamical systems. It contains contributions to Teichmuller dynamics, interval
I. Assani
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Geometric and Ergodic Theory of Hyperbolic Dynamical Systems [PDF]
Current Developments in Mathematics, 1998 L. Young
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Dynamical Systems, Ergodic Theory, and Probability: in Memory of Kolya Chernov [PDF]
, 2017 A. Blokh +4 more
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SIAM Journal on Applied Dynamical Systems, 2022 We show that singular stochastic delay differential equations (SDDEs) induce cocycle maps on a field of Banach spaces. A general Multiplicative Ergodic Theorem on fields of Banach spaces is proved and applied to linear SDDEs.
Mazyar Ghani Varzaneh +2 more
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Pure point spectrum for dynamical systems and mean, Besicovitch and Weyl almost periodicity
Ergodic Theory and Dynamical Systems, 2023 We consider metrizable ergodic topological dynamical systems over locally compact, $\sigma $ -compact abelian groups. We study pure point spectrum via suitable notions of almost periodicity for the points of the dynamical system.
D. Lenz +2 more
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Bridging Data Science and Dynamical Systems Theory [PDF]
, 2020 This short review describes mathematical techniques for statistical analysis and prediction in dynamical systems. Two problems are discussed, namely (i) the supervised learning problem of forecasting the time evolution of an observable under potentially ...
Tyrus Berry, D. Giannakis, J. Harlim
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Stochastic homogenization of maximal monotone relations and applications
Networks and Heterogeneous Media, 2018 We study the homogenization of a stationary random maximal monotone operator on a probability space equipped with an ergodic dynamical system. The proof relies on Fitzpatrick's variational formulation of monotone relations, on Visintin's scale ...
Luca Lussardi +2 more
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Ergodic optimization in dynamical systems [PDF]
Ergodic Theory and Dynamical Systems, 2017 Ergodic optimization is the study of problems relating to maximizing orbits and invariant measures, and maximum ergodic averages. An orbit of a dynamical system is called $f$ -maximizing if the time average of the real-valued function $f$ along the orbit
O. Jenkinson
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Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling [PDF]
QuantumA key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient.
Tara Kalsi +2 more
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