This paper is a review of the present status of studies relating to occurrence of deterministic chaos and its characterization in one-dimensional maps. As our primary aim is to introduce the nonspecialists into this fascinating world of chaos we start from very elementary concepts and give sufficient arguments for clarity of ideas. The two main scenarios during onset of chaos viz. the period doubling and intermittency are dealt with in detail. Although the logistic map is often discussed by way of illustration, a few more interesting maps are mentioned towards the end.

We discuss the classical mechanics of relativistic systems containing any number of particles with direct interaction. We continue our previous approach of restricting the observables to gauge invariant variables. As a preliminary we show how to constructN-particle mass shell constraints. Physical momentum and position variables are constructed in consonance with nonsuperluminality and relativity and consistent with a slightly weakened separability which allows the position four vector of separated particles to differ from the canonical coordinate four vector by a constant term which depends on its history but does not affect future dynamics. The formalism is mathematically consistent though slightly more complicated than previous attempts in this direction.

Classical and quantum cosmological aspects for (n + 2) dimensional anisotropic spherically symmetric space-time with topology of (n + 1) spaceS¹×Sⁿ have been studied. The Lorentzian field equations are reduced to an autonomous system by a change of field variables and are discussed near the critical points. The path integral expression for propagation amplitude is converted to a single ordinary integration over the lapse function by the usual technique and is evaluated in terms of Bessel functions.

We present further analysis of the structure functions at low-x using the approximate solutions of Altarelli-Parisi equations recently reported by us. We also compare our results with non-perturbative and non-linear evolutions.

The nuclear molecular resonances observed in α+¹²C and α+¹⁶O systems are described in a diatomic-like molecular picture using a Morse-type bonding potential. The depths of the bonding potentials are found to be 11.5 MeV and 11 MeV respectively, with long range of about 15 fm. Both the bound and resonance states of these potentials are calculated which compare quite well with the observed states. The diatomic-like rotational and vibrational picture of the quasi-molecular states proposed earlier for¹²C+¹²C system system is found to be quite valid for α+¹²C and α+¹⁶O systems. In these two systems, the rotational vibrational characteristics are equally well pronounced as in the¹²C+¹²C system.

Total (elastic+inelastic) cross sections fore⁻-O,e⁻-O₂ ande⁻-O₃ scattering have been calculated at sample energies between 100 and 1000eV. The basice⁻-O atom scattering amplitudes are obtained from the partial wave analysis with a complex optical potential. Thee⁻-O₂ ande⁻-O₃ cross-sections are obtained through the independent atom model. Oure⁻-O₂ cross-sections reproduce the experimental data quite well. Adequate comparisons are made in all the three cases.

Relative differential cross-sections for the elastic scattering of electrons from benzene have been measured at incident energies 300, 500, 700 and 900eV and for scattering angles between 30° and 120°. The results are discussed and compared with the independent atom model (IAM) calculations. Two different sets of scattering amplitudes for the constituent atoms of benzene were used in these calculations, one obtained from first Born approximation and the other from partial wave analysis of the Dirac equation. Only the static interaction was taken into account in the calculations. The higher the incident energy, the better is the observed agreement between experiment and theory. This indicates that at higher energies, absorption, exchange and polarization effects are not significant as compared to the static interaction and that the IAM satisfactorily predicts the interference of scattering from the individual atoms of C₆H₆.

TheR-matrix method is used to calculate cross-sections for the photoionization of Ne-like Fe¹⁶⁺ from ground 2s²2p⁶¹S^e and excited states belonging to 2s2p⁶ 3l and 2s²2p⁵ 3l configurations. Configuration interaction wavefunctions are used to represent two target states of Fe¹⁷⁺ ion retained in theR-matrix expansion. The cross-sections are obtained as a function of kinetic energy (ε_k) of the ejected electron from 10 to 24 Ry. For low kinetic energy the cross-sections show series of Rydberg states which converge onto²S^e threshold Fe¹⁷⁺. The calculations are carried out in the LS coupling.