Generalized Lorenz Equations for Acoustic-Gravity Waves in the Atmosphere. Attractors Dimension, Convergence and Homoclinic Trajectories

G. A. Leonov

doi:10.3934/cpaa.2017111

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2017, Volume 16, Issue 6: 2253-2267. Doi: 10.3934/cpaa.2017111

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Generalized Lorenz Equations for Acoustic-Gravity Waves in the Atmosphere. Attractors Dimension, Convergence and Homoclinic Trajectories

G. A. Leonov^,

Saint-Petersburg State University, Universitetsky pr. 28, Saint-Petersburg, Russia, 198504

* Corresponding author
* Corresponding author

Received: April 2017

Revised: May 2017

Published: September 2017

G. A. Leonov is supported by the Russian Science Foundation project no. 14-21-00041.

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Abstract

Attractors dimension of Lorenz-Stenflo system is estimated. Convergence criteria are proved. Fishing principle for existence of homoclinic trajectory is applied.

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Mathematics Subject Classification: Primary: 37L30; Secondary: 37C29.

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Figure 13. Separatrix $X(t,s)^+$, $s\in[0,s_0]$.

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Figure 14. Separatrix $X(t,s)^+$, $s=s_0$.

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References

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[10]	G. A. Leonov, Rössler systems: estimates for the dimension of attractors and homoclinic orbits, Dokl. Math., 89 (2014), 369-371.
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