In this paper, Hamiltonian monodromy is addressed from the point of view of geometric quantization, and various differential geometric aspects thereof are dealt with, all related to holonomies of suitable flat connections. In the case of completely integrable Hamiltonian systems with two degrees of freedom, a link is established between monodromy and (2-level) theta functions, by resorting to t...

Global conformal invariance (GCI) of quantum field theory (QFT) in two and higher space–time dimensions implies the Huygens’ principle, and hence, rationality of correlation functions of observable fields [29]. The conformal Hamiltonian H has discrete spectrum assumed here to be finitely degenerate. We then prove that thermal expectation values of field products on compactified Minkowski space ...

‎By the Mordell‎- ‎Weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎This paper studies the rank of the family Epq:y2=x3-pqx of elliptic curves‎, ‎where p and q are distinct primes‎. ‎We give infinite families of elliptic curves of the form y2=x3-pqx with rank two‎, ‎three and four‎, ‎assuming a conjecture of Schinzel ...

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.

We consider solutions of the KP hierarchy which are elliptic functions $x=t_1$. It is known that their poles as $t_2$ move particles Calogero-Moser model. extend this correspondence to level hierarchies and find Hamiltonian $H_k$ model governs dynamics with respect $k$-th hierarchical time. The Hamiltonians obtained coefficients expansion spectral curve near marked point in Baker-Akhiezer funct...

The objective of this article is to present geometric and numerical techniques developed to study the orbit transfer between Keplerian elliptic orbits in the two-body problem or between quasi-Keplerian orbits in the EarthMoon transfer when low propulsion is used. We concentrate our study on the energy minimization problem. From Pontryagin’s maximum principle, the optimal solution can be found s...

We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T3 on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S1 action on the union of the non-degener...