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Some applications of Hausdorff dimension inequalities for ordinary differential equations. (English) Zbl 0622.34040
Author’s summary: ”Upper bounds are obtained for the Hausdorff dimension of compact invariant sets of ordinary differential equations which are periodic in the independent variable. From these are derived sufficient conditions for dissipative analytic n-dimensional \(\omega\)-periodic differential equations to have only a finite number of \(\omega\)-periodic solutions. For autonomous equations the same conditions ensure that each bounded semi-orbit converges to a critical point. These results yield some information about the Lorenz equation and the forced Duffing equation.”
Reviewer: H.Hochstadt

MSC:
34C25 Periodic solutions to ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
28D99 Measure-theoretic ergodic theory
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