Analytical study of the Lorenz system: Existence of infinitely many periodic orbits and their topological characterization
We consider the Lorenz equations, a system of three-dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been introduced in the seventies. One of the classical pro...
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| Veröffentlicht in: | Proceedings of the National Academy of Sciences - PNAS 2023-08, Vol.120 (31), p.e2205552120-e2205552120 |
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| creator | Pinsky, Tali |
| description | We consider the Lorenz equations, a system of three-dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been introduced in the seventies. One of the classical problems in dynamical systems is to relate the original equations to the geometric model. This has been achieved numerically by Tucker for the classical parameter values and remains open for general values. In this paper, we establish analytically a relation to the geometric model for a different set of parameter values that we prove must exist. This is facilitated by finding a way to apply topological tools developed for the study of surface dynamics to the more intricate case of three-dimensional flows. |
| doi_str_mv | 10.1073/pnas.2205552120 |
| format | Article |
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| subjects | Atmospheric convection Atmospheric models Differential equations Dynamical systems Lorenz equations Lorenz system Mathematical models Orbits Parameters Physical Sciences Surface dynamics Three dimensional flow Topology |
| title | Analytical study of the Lorenz system: Existence of infinitely many periodic orbits and their topological characterization |
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