Conclusion

Analytical and numerical-analytical methods of cascade theory were developed, the study was performed of multi-dimensional characteristics (lateral, angular, spatial, spatial-angular distributions of the mean number of shower particles and their fluctuations) of electron-photon and hadron cascades in cosmic rays at superhigh energies. Cascade development models convenient for applications were created. New methods for calculation of cascades in stratified X-ray emulsion chambers were elaborated and the influence of gaps of various values on the parameters of cascades detected was studied. New analytical methods to calculate fluxes of cosmic rays in the atmosphere were elaborated, which enable taking into account logarithmic growth of hadron-air nucleus interaction and allowed to suggest and substantiate a hypothesis of a change in the interaction characteristics with increasing energy.