Walter Reartes

  • Citations Per Year
Learn More
In this paper we present a new approach for finding periodic orbits in dynamical systems modeled by differential equations. It is based on the Homotopy Analysis Method (HAM) but it differs from the usual way it is applied. We apply the HAM to construct approximations of a formal series solution of the equation. These approximations exist for any value of(More)
In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel Hilbert space. A definition of the Feynman propagator, based on the reproducing property of this space, is proposed.(More)
Communicated by Vasil V. Tsanov Abstract. In this paper we develop the quantization of a particle in the plane under the influence of a perpendicular magnetic field using the geometric quantization with half–forms in Hilbert space of holomorphic functions. An original coordinate transformation is applied to convert the problem into a system of harmonic(More)
In this paper we apply the homotopy analysis method (HAM) to study the van der Pol equation with a linear delayed feedback. The paper focuses on the calculation of periodic solutions and associated bifurcations, Hopf, double Hopf, Neimark-Sacker, etc. In particular we discuss the behavior of the systems in the neighborhoods of double Hopf points. We(More)
  • 1