The computation of Lyapunov quantities is closely connected with the important in engineering mechanics question of dynamical system behavior near to boundary of the stability domain. Followed by the work of Bautin [1], one differs "safe" or "dangerous" boundaries, a slight shift of which implies a small (invertible) or noninvertible changes of system status, respectively. Such changes correspo...

Finite entropy thermal systems undergo Poincaré recurrences. In the context of field theory, this implies that at finite temperature, timelike two-point functions will be quasi-periodic. In this note we attempt to reproduce this behavior using the AdS/CFT correspondence by studying the correlator of a massive scalar field in the bulk. We evaluate the correlator by summing over all the SL(2, Z) ...

We briefly describe the importance of division algebras and Poincaré conjecture in both mathematical and physical scenarios. Mathematically, we argue that using the torsion concept one can combine the formalisms of division algebras and Poincaré conjecture. Physically, we show that both formalisms may be the underlying mathematical tools in special relativity and cosmology. Moreover, we explore...

In this research we discussed about the solution of KdV equation using Homotopy Perturbation method. The that describing water wave solved by mixing method between and was built with embedding parameter p∈[0,1] which undergoes a deformation process from linear problems to nonlinear assumed is expressed in form power series p up third order. result show each order obtained resonance term. for ha...