Dynamical systems and ergodic theory

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Distal systems in topological dynamics and ergodic theory [PDF]

Ergodic Theory and Dynamical Systems, 2022
AbstractWe generalize a result of Lindenstrauss on the interplay between measurable and topological dynamics which shows that every separable ergodic measurably distal dynamical system has a minimal distal model. We show that such a model can, in fact, be chosen completely canonically.
NIKOLAI EDEKO, HENRIK KREIDLER
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Equipping mathematical models for hospital dynamics using information theory [PDF]

npj Digital Medicine
We propose metrics from information theory to characterize the clinical and operational dynamics of hospitals. Ergodicity, the equality of time- and space-averages within a dynamical system, ensures its stationarity.
Jeremy A. Balch +15 more
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Bowen’s Formula for a Dynamical Solenoid [PDF]

Entropy
More than 50 years ago, Rufus Bowen noticed a natural relation between the ergodic theory and the dimension theory of dynamical systems. He proved a formula, known today as the Bowen’s formula, that relates the Hausdorff dimension of a conformal repeller
Andrzej Biś +2 more
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Applications of Entropy in Data Analysis and Machine Learning: A Review [PDF]

Entropy
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory, Ergodic Theory and
Salomé A. Sepúlveda-Fontaine, José M. Amigó +1 more
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Dynamical quantum ergodicity from energy level statistics

Physical Review Research, 2023
Ergodic theory provides a rigorous mathematical description of chaos in classical dynamical systems, including a formal definition of the ergodic hierarchy. How ergodic dynamics is reflected in the energy levels and eigenstates of a quantum system is the
Amit Vikram, Victor Galitski
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Review article: Hilbert problems for the climate sciences in the 21st century – 20 years later [PDF]

Nonlinear Processes in Geophysics, 2020
The scientific problems posed by the Earth's atmosphere, oceans, cryosphere – along with the land surface and biota that interact with them – are central to major socioeconomic and political concerns in the 21st century.
M. Ghil, M. Ghil, M. Ghil
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Theory of Ergodic Quantum Processes

Physical Review X, 2021
The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels.
Ramis Movassagh, Jeffrey Schenker
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Fractional stochastic vibration system under recycling noise

Frontiers in Physics, 2023
The fractional stochastic vibration system is quite different from the traditional one, and its application potential is enormous if the noise can be deployed correctly and the connection between the fractional order and the noise property is unlocked ...
Jian-Gang Zhang, Fang Wang, Hui-Nan Wang
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Stability Assessment of Stochastic Differential-Algebraic Systems via Lyapunov Exponents with an Application to Power Systems

Mathematics, 2020
In this paper, we discuss stochastic differential-algebraic equations (SDAEs) and the asymptotic stability assessment for such systems via Lyapunov exponents (LEs).
Andrés González-Zumba +3 more
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Typical = Random

Axioms, 2023
This expository paper advocates an approach to physics in which “typicality” is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed.
Klaas Landsman
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