Related papers: Waist theorems for Tonelli systems in higher dimen…
Considering the fluctuations of spectral functions, we prove that if chaotic systems fulfill the Bohigas-Gianonni-Schmit (BGS) conjecture, which relates their spectral statistics to that of random matrices, therefore by virtue of Gutzwiller…
In the present paper we study the causal structure of a topological black hole presented by Mann R. B. JHEP 06, 075 (2009) by mean the standard Lagrangian procedure, which allow us analyze qualitatively the behavior of test particles using…
In this paper, we use the restricted three body problem in the binary stellar systems, taking photogravitational effects of both the stars. The aim of this study is to investigate the motion of the infinitesimal mass in the vicinity of the…
Let $-1<\lambda<1$ and $f:[0,1)\to\mathbb{R}$ be a piecewise $\lambda$-affine map, that is, there exist points $0=c_0<c_1<\cdots <c_{n-1}<c_n=1$ and real numbers $b_1,\ldots,b_n$ such that $f(x)=\lambda x+b_i$ for every $x\in…
In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian…
In this work, we study the gravitational waveforms from the periodic orbits of a massive particle around a dyonic ModMax black hole. We begin with a brief analysis of the spacetime and then examine how its parameters influence the dynamics…
It is proved, using the curved line element of a spherically symmetric charged object in general relativity and the Schwinger discharge mechanism of quantum field theory, that the orbital periods $T_{\infty}$ of test particles around…
An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same…
A finit periodic $\delta-\delta'$ comb was solved by the help of both classical approach based on a direct solving of a Sr\"{odinger} equation and a quantum wave impedance method. It was demonstrated that the violation of a periodicity…
In this paper we study the existence and multiplicity of periodic orbits of exact magnetic flows with energy levels above the Ma\~{n}\'{e} critical value of the universal cover on a non-compact manifold from the viewpoint of Morse theory.
We consider faithful actions of simple algebraic groups on self-dual irreducible modules, and on the associated varieties of totally singular subspaces, under the assumption that the dimension of the group is at least as large as the…
We prove that for a certain class of closed monotone symplectic manifolds any Hamiltonian diffeomorphism with a hyperbolic fixed point must necessarily have infinitely many periodic orbits. Among the manifolds in this class are complex…
The Horndeski Lagrangian brings together all possible interactions between gravity and a scalar field that yield second-order field equations in four-dimensional spacetime. As originally proposed, it only addresses phenomenology without…
We present a general semiclassical theory of the orbital magnetic response of noninteracting electrons confined in two-dimensional potentials. We calculate the magnetic susceptibility of singly-connected and the persistent currents of…
The thesis is divided into two parts. In the first part the low-energy limit of quantum gravity is analysed, whereas in the second we deal with the high-energy domain. In the first part, by applying the effective field theory point of view…
We investigate the dynamics in the logarithmic galactic potential with an analytical approach. The phase-space structure of the real system is approximated with resonant detuned normal forms constructed with the method based on the Lie…
A level orbit of a mechanical Hamiltonian system is a solution of Newton equation that is contained in a level set of the potential energy. In 2003, Mark Levi asked for a characterization of the smooth potential energy functions on the…
This article investigates stationary surfaces with boundaries, which arise as the critical points of functionals dependent on curvature. Precisely, a generalized "bending energy" functional $\mathcal{W}$ is considered which involves a…
We consider a natural class of time-periodic infinite-dimensional nonlinear Hamiltonian systems modelling the interaction of a classical mechanical system of particles with a scalar wave field. When the field is defined on a space torus…
We analyze the topological structure of the Nehari set for a class of functionals depending on a real parameter $\lambda$, and having two degrees of homogeneity. A special attention is paid to the extremal parameter $\lambda^*$, which is…