Some applications of Hausdorff dimension inequalities for ordinary differential equations
- 1 January 1986
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 104 (3-4) , 235-259
- https://doi.org/10.1017/s030821050001920x
Abstract
Synopsis: 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 ω-periodic differential equations to have only a finite number of ω-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.This publication has 11 references indexed in Scilit:
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