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We consider the stability of periodic map with period-$2$ in linear fractional difference equations where the function is $f(x)=ax$ at even times and $f(x)=bx$ at odd times. The stability of such a map for an integer order map depends on…
In this paper we have considered higher order two dimensional coupled system of non-linear ordinary differential equations. We have given necessary and sufficient conditions on the non-linear functions such that the solutions pair oscilla
Nonlinear second-order ordinary differential equations are common in various fields of science, such as physics, mechanics and biology. Here we provide a new family of integrable second-order ordinary differential equations by considering…
It is the second article of a series whose final goal is the stabilization of the twisted trace formula. Over a non archimedean field, we define (after Arthur) wheighted orbital integrals and their stable and endoscopic versions. We state…
Let $q$ be an odd prime power. Let $f\in \mathbb{F}_q[x]$ be a polynomial having degree at least $2$, $a\in \mathbb{F}_q$, and denote by $f^n$ the $n$-th iteration of $f$. Let $\chi$ be the quadratic character of $\mathbb{F}_q$, and…
We consider a completely integrable system of differential equations in arbitrary dimensions whose phase space contains an open set foliated by periodic orbits. This research analyzes the persistence and stability of the periodic orbits…
In autonomous differential equations where a single first integral is present, periodic orbits are well-known to belong to one-parameter families, parameterized by the first integral's values. This paper shows that this characteristic…
We prove existence of small amplitude, 2 pi/omega -periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency omega belonging to a Cantor-like set of positive measure and…
We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed…
This work introduces a new set of orbital elements to fully represent the zonal harmonics problem around an oblate celestial body. This new set of orbital elements allows to obtain a complete linear system for the unperturbed problem and,…
A semiclassical analysis is made of the origin of an undulating pattern in the smoothed level density for a reflection-asymmetric superdeformed oscillator potential. It is suggested that, when the octupole-type deformation increases, an…
We present a new method for computing orbits in the perturbed two-body problem: the position and velocity vectors of the propagated object in Cartesian coordinates are replaced by eight orbital elements, i.e., constants of the unperturbed…
We present an adaptation of a relatively simple topological argument to show the existence of many periodic orbits in an infinite dimensional dynamical system, provided that the system is close to a one-dimensional map in a certain sense.…
Using Gutzwiller's semiclassical periodic-orbit theory we demonstrate universal behaviour of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in…
In this paper, convergent, multi-infinite, series solutions are derived for the homoclinic orbits of a canonical fourth-order ODE system, in both reversible and non-reversible cases. This ODE includes traveling-wave reductions of many…
The Riccati equation method is used to establish an oscillatory and a non oscillatory criteria for nonhomogeneous linear systems of two first-order ordinary differential equations. It is shown that the obtained oscillatory criterion is a…
When using atom-centered integration grids, the portion of the grid that belongs to a certain atom also moves when this atom is displaced. In the paper, we investigate the moving-grid effect in the calculation of the harmonic vibrational…
This work is based on the letter Phys. Lett. B, 865, 139484 (2025), where we developed the analytical expression of the coordinate time in terms of the eccentric anomaly at the second post-Newtonian order in General Relativity for a compact…
In this paper, we discuss the definition of Q factor for nonlinear oscillators. While available definitions of Q are often limited to linear resonators or oscillators with specific topologies, our definition is applicable to any oscillator…
In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce two types of nonlocal transformations which relate specific classes of nonlinear…