Results 1 to 10 of about 1,703,724 (178)
DIFFERENTIABLE DYNAMICAL SYSTEMS [PDF]
Bulletin of the American Mathematical Society, 1967 This is a survey article on the area of global analysis defined by differentiable dynamical systems or equivalently the action (differentiable) of a Lie group G on a manifold M. An action is a homomorphism G→Diff(M) such that the induced map G×M→M is differentiable.
S. Smale
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Complexities of differentiable dynamical systems [PDF]
Journal of Mathematical Physics, 2020 We define the notion of localizable property for a dynamical system. Then, we survey three properties of complexity and relate how they are known to be typical among differentiable dynamical systems. These notions are the fast growth of the number of periodic points, the positive entropy, and the high emergence.
P. Berger
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Classical Fisher information for differentiable dynamical systems [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2023 Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a form of uncertainty.
Mohamed Sahbani +2 more
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Landau: A Language for Dynamical Systems with Automatic Differentiation [PDF]
Journal of Mathematical Sciences, 2020 Most numerical solvers used to determine free variables of dynamical systems rely on first-order derivatives of the state of the system w.r.t. the free variables. The number of the free variables can be fairly large. One of the approaches of obtaining those derivatives is the integration of the derivatives simultaneously with the dynamical equations ...
Dmitry Pavlov, Ivan Dolgakov
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Differentiable dynamical systems and the problem of turbulence [PDF]
Bulletin of the American Mathematical Society, 1981 Summary: The paper is a review presented at the Symposium on the Mathematical Heritage of Henry Poincaré in 1980. The author discusses different theories of turbulence. He explains the way dynamical systems appear in the study of Navier-Stokes equation and describes the connection between the turbulence and the ``strange'' attractors theory. The author
D. Ruelle
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Geometric Neural Ordinary Differential Equations: From Manifolds to Lie Groups [PDF]
EntropyNeural ordinary differential equations (neural ODEs) are a well-established tool for optimizing the parameters of dynamical systems, with applications in image classification, optimal control, and physics learning.
Yannik P. Wotte +2 more
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Ergodic theory of differentiable dynamical systems [PDF]
Publications mathématiques de l'IHÉS, 1979 Iff is a C1 + ɛ diffeomorphism of a compact manifold M, we prove the existence of stable manifolds, almost everywhere with respect to everyf-invariant probability measure on M. These stable manifolds are smooth but do not in general constitute a continuous family.
D. Ruelle
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Discrete and Continuous Dynamical Systems. Series A, 2019 In this paper, we establish a KAM-theorem about the existenceof invariant tori in non-conservative dynamical systems with finitely differentiable vector fields and multiple degeneracies under the assumption that theintegrable part is finitely ...
Xuemei Li, Zaijiu Shang
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Homomorphisms of differentiable dynamical systems [PDF]
Kyoto Journal of Mathematics, 1974 Toshio Niwa
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On Differentiation and Homeostatic Behaviours of Boolean Dynamical Systems [PDF]
, 2006 We study rules proposed by the biologist R. Thomas relating the structure of a concurrent system of interacting genes (represented by a signed directed graph called a regulatory graph) with its dynamical properties. We prove that the results in [10] are stable under projection, and this enables us to relax the assumptions under which they are valid ...
Paul Ruet, Elisabeth Remy
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