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Attractor

About: Attractor is a research topic. Over the lifetime, 21132 publications have been published within this topic receiving 523966 citations.


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Book
01 Jan 1987
TL;DR: The second edition of the Navier-Stokes Equations as mentioned in this paper provides an overview of its application in a variety of problems, including the existence, uniqueness, and regularity of solutions.
Abstract: Preface to the second edition Introduction Part I. Questions Related to the Existence, Uniqueness and Regularity of Solutions: 1. Representation of a Flow: the Navier-Stokes Equations 2. Functional Setting of the Equations 3. Existence and Uniqueness Theorems (Mostly Classical Results) 4. New a priori Estimates and Applications 5. Regularity and Fractional Dimension 6. Successive Regularity and Compatibility Conditions at t=0 (Bounded Case) 7. Analyticity in Time 8. Lagrangian Representation of the Flow Part II. Questions Related to Stationary Solutions and Functional Invariant Sets (Attractors): 9. The Couette-Taylor Experiment 10. Stationary Solutions of the Navier-Stokes Equations 11. The Squeezing Property 12. Hausdorff Dimension of an Attractor Part III. Questions Related to the Numerical Approximation: 13. Finite Time Approximation 14. Long Time Approximation of the Navier-Stokes Equations Appendix. Inertial Manifolds and Navier-Stokes Equations Comments and Bibliography Comments and Bibliography Update for the Second Edition References.

1,342 citations

Book
01 Apr 1992
TL;DR: In this article, the authors present an overview of Semigroups of linear operators and their relation to a parameter of Attractors of Differentiable Semigroup and Uniform Asymptotics of Trajectories.
Abstract: Quasilinear Evolutionary Equations and Semigroups Generated by Them. Maximal Attractors of Semigroups. Attractors and Unstable Sets. Some Information on Semigroups of Linear Operators. Invariant Manifolds of Semigroups and Mapping at Equilibrium Points. Steady-state Solutions. Differentiability of Operators of Semigroups Generated by Partial Differential Equations. Semigroups Depending on a Parameter. Dependence on a Parameter of Attractors of Differentiable Semigroups and Uniform Asymptotics of Trajectories. Hausdorff Dimension of Attractors. Bibliography. Index.

1,275 citations

Journal ArticleDOI
TL;DR: A simple four-variable oscillator containing but one quadratic term produces a higher form of chaos with two (rather than one) directions of hyperbolic instability on the attractor as mentioned in this paper.

1,240 citations

Journal ArticleDOI
TL;DR: Interpretation of results in terms of 'functional sources' and 'functional networks' allows the identification of three basic patterns of brain dynamics: normal, ongoing dynamics during a no-task, resting state in healthy subjects, and hypersynchronous, highly nonlinear dynamics of epileptic seizures and degenerative encephalopathies.

1,226 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023858
20221,819
2021926
2020961
2019929
2018963