In this paper we present two approaches to estimate the Hausdorff dimension of an invariant compact set of a dynamical system: the method of characteristic exponents (estimates of the Kaplan-Yorke type) and the method of Lyapunov functions. In the first approach, using Lyapunov's first method we exploit characteristic exponents for obtaining such estimate. A close relationship with uniform asymptotic stability hereby is established. A second bound for the Hausdorff dimension is obtained by exploiting Lyapunov's direct method and thus relies on the use of certain Lyapunov functions.
|Title of host publication||Control of oscillations and chaos : 2000 2nd international conference, July 5-7, St. Petersburg, Russia|
|Place of Publication||Piscataway|
|Publisher||Institute of Electrical and Electronics Engineers|
|Publication status||Published - 2000|