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Abstract.We prove, among others, the following relations between notions of chaos for continuous maps of the interval: (i) A map / is not chaotic in the sense of Li and Yorke iff / restricted to the set of its w-limit points is stable in the sense of Ljapunov. (ii) The topological entropy of / is zero iff / restricted to the set of chain recurrent points is not chaotic in the sense of Li and Yorke, and this is iff every trajectory is approximable by trajectories of periodic intervals.

The electronic structure of LiCu 2 O 2 was studied using x-ray emission ͑Cu L ␣ , O K ␣ ) and photoelectron spectroscopy ͑valence band and core levels͒ as well as band-structure calculations in terms of local spindensity approximation ͑LSDA͒ and LSDAϩU approaches. According to the x-ray-emission and photoelectron spectra the valence states of the Cu atoms are found to be mixed, i.e., 2ϩ and 1ϩ. The LSDA calculations are contradictory to the experimental data and cannot reproduce the band gap and magnetic properties of LiCu 2 O 2 . The LSDAϩU calculations describe the insulator and antiferromagnetic properties much better but the overestimation of the screened Coulomb parameter U leads to a binding-energy shift of the Cu II 3d states and this distorts the proper modeling of the valence-band structure. The magnetic structure of LiCu 2 O 2 is discussed, taking our LSDAϩU band-structure calculations into account. ͓S0163-1829͑98͒04108-3͔ D. A. ZATSEPIN et al.

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