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This paper surveys results of the authors and others conceming estimates for the Hausdorff dimension of strange attractors, particularly in the case of (generalized) Lorenz systems and Rössler systems. A key idea is the interpretation of Hausdorff measure as an analogue of a Lyapunov function.
When symmetries of differential equations are applied, various types of associated systems of equations appear. Compatibility conditions of the associated systems expressed in the form of differential equations inherit Lie symmetries of the initial equations. Invariant solutions to compatibility...
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