We perform a numerical study of the breakdown of hyperbolicity of quasi-periodic attractors in the dissipative standard map. In this study, we compute the quasi-periodic attractors together with their stable and tangent bundles. We observe that the loss of normal hyperbolicity comes from the collision of the stable and tangent bundles of the quasi-periodic attractor. We provide numerical eviden...

Vidya Venkatachalam and Jorge L. Aravena Department of Electrical and Computer Engineering Louisiana State University, Baton Rouge, LA 70803-5901 Tel : (504) 388-5537, Fax : (504) 388-5200 Email : [email protected] ABSTRACT This paper presents results on the multiresolution analysis of nonstationary signals with the objective of detecting underlying periodic phenomena. Wavelet packet analysis ...

The relation between recurrent behavior and the absence of a stable periodic orbit is discussed for unimodal maps. Almost all periodic maps are non-recurrent and almost all non-periodic are recurrent. Still one feels that the critical orbit cannot accumulate to quickly on the critical point, if it wants to avoid an asymptotic periodic behavior. We obtain exponential bounds of this type in terms...

An element x of the ring R is called periodic if there exist distinct positive integers m, n such that xm = xn; and x is potent if there exists n > 1 for which xn = x. We denote the set of potent elements by P or P(R), the set of nilpotent elements by N or N(R), the center by Z or Z(R), and the Jacobson radical by J or J(R). The ring R is called periodic if each of its elements is periodic, and...

The main objective of this study is to reduce optimal vibration suppression of Timoshenko beam under non-periodic step and impulse inputs. Cantilever beam was modeled by Timoshenko theory and finite element numerical method. Stiffness (K), mass (M), and damping (C) matrices are extracted. Then, in order to control structure vibration, piezoelectric patches were used due to simultaneous dual beh...