Unpredictability, Uncertainty and Fractal Structures in Physics
Yıl: 2021 Cilt: 3 Sayı: 2 Sayfa Aralığı: 43 - 46 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022
Unpredictability, Uncertainty and Fractal Structures in Physics
Öz: In Physics, we have laws that determine the time evolution of a given physical system, depending on its parameters and its initial conditions. When we have multi-stable systems, many attractors coexist so that their basins of attraction might possess fractal or even Wada boundaries in such a way that the prediction becomes more complicated depending on the initial conditions. Chaotic systems typically present fractal basins in phase space. A small uncertainty in the initial conditions gives rise to a certain unpredictability of the final state behavior. The new notion of basin entropy provides a new quantitative way to measure the unpredictability of the final states in basins of attraction. Simple methods from chaos theory can contribute to a better understanding of fundamental questions in physics as well as other scientific disciplines.
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- Ballentine, L. E., 1970 The statistical interpretation of quantum mechanics. Reviews of Modern Physics 42: 358.
- Bera, M. N., A. Acín, M. Ku´s, M.W. Mitchell, and M. Lewenstein, 2017 Randomness in quantum mechanics: philosophy, physics and technology. Reports on Progress in Physics 80: 124001.
- Bernal, J. D., J. M. Seoane, and M. A. F. Sanjuán, 2018 Uncertainty dimension and basin entropy in relativistic chaotic scattering. Physical Review E 97: 042214.
- Bernal, J. D., J. M. Seoane, J. C. Vallejo, L. Huang, and M. A. F. Sanjuán, 2020 Influence of the gravitational radius on asymptotic behavior of the relativistic sitnikov problem. Physical Review E 102: 042204.
- Born, M., 1969 Is classical mechanics in fact deterministic? In Physics in my Generation, pp. 78–83, Springer.
- Daza, A., B. Georgeot, D. Guéry-Odelin, A. Wagemakers, and M. A. F. Sanjuán, 2017a Chaotic dynamics and fractal structures in experiments with cold atoms. Physical Review A 95: 013629.
- Daza, A., J. O. Shipley, S. R. Dolan, and M. A. F. Sanjuán, 2018aWada structures in a binary black hole system. Physical Review D 98: 084050.
- Daza, A., A. Wagemakers, B. Georgeot, D. Guéry-Odelin, and M. A. F. Sanjuán, 2016 Basin entropy: a new tool to analyze uncertainty in dynamical systems. Scientific Reports 6: 1–10.
- Daza, A., A. Wagemakers, B. Georgeot, D. Guéry-Odelin, and M. A. F. Sanjuán, 2018b Basin entropy, a measure of final state unpredictability and its application to the chaotic scattering of cold atoms. In Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives, pp. 9–34, Springer.
- Daza, A., A.Wagemakers, and M. A. F. Sanjuán, 2017bWada property in systems with delay. Communications in Nonlinear Science and Numerical Simulation 43: 220–226.
- Daza, A., A.Wagemakers, and M. A. F. Sanjuán, 2018c Ascertaining when a basin is Wada: the merging method. Scientific Reports 8: 1–8.
- Daza, A., A. Wagemakers, M. A. F. Sanjuán, and J. A. Yorke, 2015 Testing for basins of Wada. Scientific Reports 5: 1–7.
- Feynman, R. P., R. B. Leighton, and M. L. Sands, 1963 The Feynman Lectures on Physics. Vol. I Mainly Mechanics, Radiation and Heat, volume 1. Addison-Wesley, Reading, Massachusetts.
- Kennedy, J. and J. A. Yorke, 1991 Basins of Wada. Physica D: Nonlinear Phenomena 51: 213–225.
- Nieto, A. R., E. E. Zotos, J. M. Seoane, and M. A. F. Sanjuán, 2020 Measuring the transition between nonhyperbolic and hyperbolic regimes in open hamiltonian systems. Nonlinear Dynamics 99: 3029–3039.
- Nusse, H. E. and J. A. Yorke, 1996Wada basin boundaries and basin cells. Physica D: Nonlinear Phenomena 90: 242– 261.
- Wagemakers, A., A. Daza, and M. A. F. Sanjuan, 2021 How to detect Wada basins. Discrete and Continuous Dynamical Systems B 26(1): 717–739.
- Wagemakers, A., A. Daza, and M. A. F. Sanjuán, 2020 The saddle-straddle method to test for Wada basins. Communications in Nonlinear Science and Numerical Simulation 84: 105167.
APA | SANJUAN M (2021). Unpredictability, Uncertainty and Fractal Structures in Physics. , 43 - 46. |
Chicago | SANJUAN MIGUEL A. F. Unpredictability, Uncertainty and Fractal Structures in Physics. (2021): 43 - 46. |
MLA | SANJUAN MIGUEL A. F. Unpredictability, Uncertainty and Fractal Structures in Physics. , 2021, ss.43 - 46. |
AMA | SANJUAN M Unpredictability, Uncertainty and Fractal Structures in Physics. . 2021; 43 - 46. |
Vancouver | SANJUAN M Unpredictability, Uncertainty and Fractal Structures in Physics. . 2021; 43 - 46. |
IEEE | SANJUAN M "Unpredictability, Uncertainty and Fractal Structures in Physics." , ss.43 - 46, 2021. |
ISNAD | SANJUAN, MIGUEL A. F.. "Unpredictability, Uncertainty and Fractal Structures in Physics". (2021), 43-46. |
APA | SANJUAN M (2021). Unpredictability, Uncertainty and Fractal Structures in Physics. Chaos Theory and Applications, 3(2), 43 - 46. |
Chicago | SANJUAN MIGUEL A. F. Unpredictability, Uncertainty and Fractal Structures in Physics. Chaos Theory and Applications 3, no.2 (2021): 43 - 46. |
MLA | SANJUAN MIGUEL A. F. Unpredictability, Uncertainty and Fractal Structures in Physics. Chaos Theory and Applications, vol.3, no.2, 2021, ss.43 - 46. |
AMA | SANJUAN M Unpredictability, Uncertainty and Fractal Structures in Physics. Chaos Theory and Applications. 2021; 3(2): 43 - 46. |
Vancouver | SANJUAN M Unpredictability, Uncertainty and Fractal Structures in Physics. Chaos Theory and Applications. 2021; 3(2): 43 - 46. |
IEEE | SANJUAN M "Unpredictability, Uncertainty and Fractal Structures in Physics." Chaos Theory and Applications, 3, ss.43 - 46, 2021. |
ISNAD | SANJUAN, MIGUEL A. F.. "Unpredictability, Uncertainty and Fractal Structures in Physics". Chaos Theory and Applications 3/2 (2021), 43-46. |