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RIDDLED BASINS
Abstract
Theory and examples of attractors with basins which are of positive measure, but contain no open sets, are developed; such basins are called riddled. A theorem is established which states that riddled basins are detected by normal Lyapunov exponents. Several examples, both mathematically rigorous and numerical, motivated by applications in the literature, are presented.
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Cited by
Fundamentals of synchronization in chaotic systems, concepts, and applications
Pecora, L. M., Carroll, T. L., Johnson, G. A., Mar, D. J., & Heagy, J. F. (1997) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.166278 · Cited by 862
Synchronous chaos in coupled oscillator systems
Heagy, J. F., Carroll, T. L., & Pecora, L. M. (1994) · Physical Review E · doi:10.1103/physreve.50.1874 · Cited by 462
Amplitude death: The emergence of stationarity in coupled nonlinear systems
Saxena, G., Prasad, A., & Ramaswamy, R. (2012) · Physics Reports · doi:10.1016/j.physrep.2012.09.003 · Cited by 375
Permanence via invasion graphs: incorporating community assembly into modern coexistence theory
Hofbauer, J., & Schreiber, S. J. (2022) · Journal of Mathematical Biology · doi:10.1007/s00285-022-01815-2 · Cited by 35
Metadata
- Authors
- ALEXANDER, J. C., YORKE, J. A., YOU, Z., & KAN, I.
- Venue
- International Journal of Bifurcation and Chaos
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 1992-12
- Volume
- 02
- Issue
- 04
- Pages
- 795-813
- ISSN
- 0218-1274 (ISSN-L)
- 1793-6551
- OpenAlex
- W4256560209
- Cited by
- 406
- References
- 0
- FWCI
- 13.58
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: RIDDLED BASINS. https://app.cochat.ai/papers/10.1142/s0218127492000446
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- ALEXANDER, J. C., YORKE, J. A., YOU, Z., & KAN, I. (1992). RIDDLED BASINS. International Journal of Bifurcation and Chaos. https://doi.org/10.1142/s0218127492000446
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