We present Poincare invariant domain wall (“3-brane”) solutions to some 5-dimensional effective theories which can arise naturally in string theory. In particular, we find theories where Poincare invariant solutions exist for arbitrary values of the brane tension, for certain restricted forms of the bulk interactions. We describe examples in string theory where it would be natural for the quant...

We identify an effective proxy for the analytically-unknown second integral of motion (I_2) rotating barred or tri-axial potentials. Planar orbits a given energy follow tight sequence in space time-averaged angular momentum and its amplitude fluctuation. The monotonically traces main orbital families Poincare map, even presence resonant chaotic orbits. This behavior allows us to define "Calibra...

In this paper, the dynamic characteristics of fractional Duffing system are analyzed and studied by using improved short memory principle method. This method has small amount calculation high precision, can effectively improve problem large caused order. The influence frequency change on performance is nonlinear analysis methods, such as Phase Portrait, Poincare Map Bifurcation Diagram. Moreove...

Poincar6 often insisted existence in mathematics means logical con-sistency, and formal logic ia the sole guarantor of rigor. The paper joins thisto his view of intuition and his own mathematics. It looks at predicativity andthe infinity Poincar^'s early endorsement of the axiom of choice, and Cantor'sset theory versus Zermelo's axioms. PoincarS discussed constructivism sympa-<l...

Mapping degree, intersection number, and the index of a zero of a vector field are defined. The Poincare-Hopf theorem, which states that under reasonable conditions the sum of the indices of a vector field equals the Euler characteristic of the manifold, is proven. Some consequences are discussed.

A perturbation method, the Lindstedt-Poincare method, is used to obtain the asymptotic expansions of the solutions of a nonlinear differential equation arising in general relativity. The asymptotic solutions contain no secular term, which overcomes a defect in Khuri’s paper. A technique of numerical order verification is applied to demonstrate that the asymptotic solutions are uniformly valid f...

6 H. Poincare, Meth. Nouv., 1 (1892), chap. III; G. D. Birkhoff, loc. cit.' 6 H. Poincar6, op. cit., 2 (1893), chap. XVII. The figure given by Poincar6 assumes that p is positive. However, the case of a negative p may be reduced to the case of a positive p, as seen from (6) by writing v + 1/27 for v. M. J. 0. Strutt, Math. Ann., 99, 625-628 (1928). 8 Cf. A. Wintner, Bull. Astr., 9, 251-253 (193...