Results 1 to 10 of about 1,770,232 (295)
Complexities of differentiable dynamical systems [PDF]
Journal of Mathematical Physics, 2019 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.
P. Berger
semanticscholar +6 more sources
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 ...
Mohamed Sahbani +2 more
semanticscholar +4 more sources
Differentiable dynamical systems and the problem of turbulence [PDF]
Bulletin of the American Mathematical Society, 1981 1. Conservative and dissipative dynamical systems. The mathematical study of differentiable dynamical systems has its origin in the desire to understand the time evolutions which occur in nature.
D. Ruelle
semanticscholar +6 more sources
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 ...
Ivan Dolgakov, Dmitry Pavlov
openalex +5 more sources
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
doaj +2 more sources
Differentiable dynamical systems [PDF]
, 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.
Stephen T. Smale
openalex +2 more sources
Time-varying Projected Dynamical Systems with Applications to Feedback Optimization of Power Systems [PDF]
IEEE Conference on Decision and Control, 2018 This paper is concerned with the study of continuous-time, non-smooth dynamical systems which arise in the context of time-varying non-convex optimization problems, as for example the feedback-based optimization of power systems. We generalize the notion
Adrian Hauswirth +4 more
semanticscholar +3 more sources
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
semanticscholar +3 more sources
DIFFERENTIABLE DYNAMICAL SYSTEMS [PDF]
Bulletin of the American Mathematical Society, 2010 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
openalex +5 more sources
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 ...
Xue-Mei Li, Zaijiu Shang
openalex +3 more sources