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Asymptotically entropy of chaotic systems increases linearly and the sensitivity to initial conditions is exponential with time: these two types of behavior are related. Such relationship is analogous to and, under specific conditions, has been shown to coincide with the Pesin identity. Numerical evidence supports the proposal that the statistical formalism can be extended to the edge of chaos by using a specific generalization of the exponential and of the Boltzmann-Gibbs entropy. We extend this picture and a Pesin-like identity to a wide class of deformed entropies and exponentials using the logistic map as a test case. The physical criterion of finite-entropy growth strongly restricts the suitable entropies. The nature and characteristics of this generalization are clarified. * )

The structural and electronic properties of some A "B' C2 ternary semiconductors with chalcopyrite structure are investigated using both the full potential linearized augmented plane wave and the ab initio pseudopotential methods. The total-energy approach is used to determine the internal distortion parameter u, discussed for these materials in terms of atomic radii. In addition, we study the band-gap anomaly, defined as the energy di6'erence with respect to the III-V binary analog compound, and the crystalfield splitting of the valence-band maximum. %e also present a total-energy study of the equilibrium structure of CdSnSb2, a potential new chalcopyrite semiconductor that might be stabilized via epitaxial growth on the well-matched InSb substrate.

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Ab initio local-density-functional calculations are presented for bulk A1N, GaN, and InN in the wurtzite, zincblende, and rocksalt structures. Structural transition pressures and deformation potentials of electronic gaps are investigated. In addition, we study the band offset at the polar (0001) and non-polar (1010) AIN/GaN interfaces. Within AIN-on-GaN epitaxial conditions, we obtain valence-band offset values close to 0.7 eV for both interfaces. From the macroscopic field appearing along the growth direction of the polar interface (tentatively attributed to AIN macroscopic polarization), an estimate of the macroscopic dielectric constant of GaN is extracted. All calculations employed conjugate-gradient total-energy minimizations, ultrasoft pseudopotentials, and plane waves at 25 Ryd cutoff.