Article
Mathematics
Rene Ruhr, Ronggang Shi
Summary: The article demonstrates that effective 2l-multiple correlations can lead to quantitative l-multiple pointwise ergodic theorems, which have various applications in different fields.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Risong Li, Tianxiu Lu, Xiaofang Yang, Yongxi Jiang
Summary: In this paper, the concepts of ergodic multi-sensitivity and strongly ergodically multi-sensitivity are introduced, with special cases proven in compact metric spaces. It is also demonstrated how the properties of different spaces and maps are related to each other.
Article
Mathematics, Applied
Luka Boc Thaler, Uros Kuzman
Summary: The article discusses the dynamics of complex rational maps on the complex plane, and shows that ergodic properties of the rational map are preserved under certain conditions by reducing their orbits to fixed positive values representing Fubini-Study distances.
ERGODIC THEORY AND DYNAMICAL SYSTEMS
(2021)
Article
Mathematics, Applied
Rocco Duvenhage
Summary: We introduce and study a class of quadratic Wasserstein distances on spaces consisting of generalized dynamical systems on a von Neumann algebra. We emphasize how symmetry of such a Wasserstein distance arises, but also study the asymmetric case. This setup is illustrated in the context of reduced dynamics, and a number of simple examples are also presented.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics
Yuri Kifer
Summary: This paper deals with the setups of fast-slow motions in continuous and discrete time. It provides conditions that simplify the setup to a specific case, and assumptions on the stochastic process allow for applications to a wide class of observables. The paper also presents an estimation of the differences between the two processes.
ISRAEL JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Daniel Lenz
Summary: The study focuses on dynamical systems (X, G, m) with specific characteristics, showing that a system has a discrete spectrum if a certain space average over the metric is a Bohr almost periodic function. This method provides insights into the behavior of general dynamical systems through metric averages.
ERGODIC THEORY AND DYNAMICAL SYSTEMS
(2021)
Article
Materials Science, Multidisciplinary
Yaroslav O. Kvashnin, Alexander N. Rudenko, Patrik Thunstrom, Malte Rosner, Mikhail Katsnelson
Summary: In this study, the magnetic and spectral properties of monolayer chromium triiodide were investigated using first-principles methods. The presence of strong local Coulomb interactions led to the formation of local magnetic moments on chromium, and the existence of local dynamical correlations modified the electronic structure of ferromagnetically ordered CrI3. The results obtained in this study were closer to experimental results compared to conventional methods.
Article
Automation & Control Systems
Chris van der Ploeg, Mohsen Alirezaei, Nathan van de Wouw, Peyman Mohajerin Esfahani
Summary: In this article, a tractable nonlinear fault estimation filter is proposed for a class of linear dynamical systems in the presence of both additive and nonlinear multiplicative faults. The proposed filter architecture combines model-based approaches and regression techniques, and the performance bounds are derived using regression operator bounds. The results show that the estimation error converges to zero with an exponential rate in the case of constant, simultaneously, and identically acting faults.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Mathematics, Applied
Kaitlyn Loyd
Summary: In this study, we examine the properties of the sequence {Ω(n)} from a dynamical point of view, where Ω(n) represents the number of prime factors of n counted with multiplicity. The results show that for any non-atomic ergodic system, the operators T-Ω(n) have the strong sweeping-out property, implying that the pointwise ergodic theorem does not hold along Ω(n). Additionally, we demonstrate that the behaviors of Ω(n) captured by the prime number theorem and Erdos-Kac theorem are disjoint, as their dynamical correlations tend to zero.
ERGODIC THEORY AND DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Applied
Claudio Bonanno, Tanja I. Schindler
Summary: This paper investigates the asymptotic behavior of Birkhoff sums for a conservative ergodic measure-preserving transformation. The results show that for systems with strong mixing assumptions, there exists a sequence and a map that guarantee the almost sure convergence of Birkhoff sums to 1 for almost all points when the measurable function belongs to L-1. In the case when the function does not belong to L-1, conditions are provided for the existence of a sequence that ensures the almost sure convergence of Birkhoff sums to 1 for almost all points.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2022)
Article
Engineering, Electrical & Electronic
Chai Wah Wu
Summary: The study shows that a combination of multiple networks can contribute to synchronization even if the coupling in a single network may not be sufficient. The effectiveness of a collection of networks to synchronize the coupled systems depends on the graph topology. If the graph sum is a directed graph whose reversal contains a spanning directed tree, the network synchronizes if the coupling is strong enough.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2021)
Article
Physics, Multidisciplinary
Peter Ashwin, Julian Newman
Summary: The paper explores the extension of physical measures to more general nonautonomous dynamical systems, with a focus on systems with autonomous limits where physical measures can be defined in relation to past limits. Two examples of systems with multiple attractors are used to demonstrate the quantification of rate-dependent tipping between chaotic attractors in terms of tipping probabilities, namely a double-scroll Chua system and a Stommel model forced by Lorenz chaos.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2021)
Article
Mathematics, Applied
Milan Korda, Didier Henrion, Igor Mezic
Summary: The paper introduces a convex-optimization-based framework for computing invariant measures of polynomial dynamical systems and Markov processes by approximating an infinite-dimensional linear program, leading to the reconstruction of measures including approximating measure support and constructing weakly converging absolutely continuous approximations. The framework also provides a method to certify the nonexistence of an invariant measure and can be adapted to compute eigenmeasures of the Perron-Frobenius operator, serving as a generalization of ergodic optimization method.
JOURNAL OF NONLINEAR SCIENCE
(2021)
Article
Mathematics
Jon Bannon, Jan Cameron, Kunal Mukherjee
Summary: This paper continues the authors' previous work on noncommutative joinings, focusing on the relative independence of W*-dynamical systems. The study proves that under certain conditions, an ergodic W*-dynamical system with a compact subsystem can be disjoint relative to its maximal compact subsystem. This generalizes previous work done by Duvenhage for abelian groups.
GROUPS GEOMETRY AND DYNAMICS
(2021)
Article
Mathematics
Bao-Wei Wang, Guo-Hua Zhang
Summary: This paper explores the dimension of the limsup set arising in general expanding dynamical systems. By assuming a dynamical ubiquity property on the system, the dimensions of X and W(T, f) are found to be related to the Bowen-Manning-McCluskey formulas. This general principle unifies and extends some known results in Diophantine approximation in dynamical systems.
MATHEMATISCHE ZEITSCHRIFT
(2021)
