On the concept of attractor
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Depending on its structure, bilinear dynamical systems may exhibit stability and attain an attractor state, but in some cases dynamical systems may demonstrate mathematical chaos.
“Depending on its structure, bilinear dynamical systems may exhibit stability and attain an attractor state (Milnor, 1985), but in some cases dynamical systems may demonstrate mathematical chaos (Lorenz, 1962).”
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- Authors
- Milnor, J.
- Affiliations
- Institute for Advanced Study (US)
- Corresponding author
- Milnor, John
- Venue
- Communications in Mathematical Physics
- Published
- 1985-06
- Volume
- 99
- Issue
- 2
- Pages
- 177-195
- ISSN
- 0010-3616 (ISSN-L)
- 1432-0916
- OpenAlex
- W1983918081
- Cited by
- 971
- References
- 0
- Citations by year
- 2026: 18 · 2025: 28 · 2024: 54 · 2023: 28 · 2022: 38 · 2021: 45 · 2020: 34 · 2019: 26 · 2018: 21 · 2017: 41 · 2016: 29 · 2015: 28 · 2014: 28 · 2013: 35 · 2012: 42
- FWCI
- 5.88
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Communications in Mathematical Physics (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Equations and Dynamical Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Controllability of Differential Equations
- Keywords
- attractors, compact dynamical systems, smooth dynamical systems, existence of attractors
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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