Related papers: Symbolic dynamics for the $N$-centre problem at ne…
We consider a nonautonomous semilinear elliptic problem where the power nonlinearity is multiplied by a discontinuous coefficient that equals one inside a bounded open set $\Omega$ and it equals minus one in its complement. In the slightly…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
In this work we provide conditions for the existence of periodic solutions to nonlinear, second-order difference equations of the form \begin{equation*} y(t+2)+by(t+1)+cy(t)=g(t,y(t)) \end{equation*} where $c\neq 0$, and…
An action minimizing path between two given configurations, spatial or planar, of the $n$-body problem is always a true -- collision-free -- solution. Based on a remarkable idea of Christian Marchal, this theorem implies the existence of…
By applying a Mawhin's continuation theorem of coincidence degree theory, we establish sufficient conditions for the existence of a periodic solution for a class of impulsive neutral differential equations. The procedure adopted in this…
Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating…
The LCDM model has been presented with a number of cosmic tensions in the face of precision cosmological data, suggesting the presence of a dynamical dark energy component. In this context, we investigate the cosmology arising from a…
We consider a specific piecewise rotation of the plane that is continuous on two half-planes, as studied by some authors like Boshernitzan, Goetz and Quas. If the angle belongs to the set $\{\frac{\pi}{2},\frac{2\pi}{3},\frac{\pi}{4}\}$, we…
We study three sub-problems of the N-body problem that have two degrees of freedom, namely the n-pyramidal problem, the planar double-polygon problem, and the spatial double-polygon problem. We prove the existence of several families of…
Examples are given of solutions of the planar N-body problem which remain the same for at least two systems of masses with the same sum and same center of mass. The least value of N achieved up to now with this property is 474, a number…
We construct countable Markov partitions for non-uniformly hyperbolic diffeomorphisms on compact manifolds of any dimension, extending earlier work of O. Sarig for surfaces. These partitions allow us to obtain symbolic coding on invariant…
In the context of the Newtonian N-body problem, we prove the existence of a partially hyperbolic motion with prescribed positive energy and any initial collisionless configuration. Moreover, it is a free time minimizer of the respective…
We present a method for proving the existence of symmetric periodic, heteroclinic or homoclinic orbits in dynamical systems with the reversing symmetry. As an application we show that the Planar Restricted Circular Three Body Problem…
We study the periodic boundary value problem associated with the second order nonlinear equation \begin{equation*} u'' + ( \lambda a^{+}(t) - \mu a^{-}(t) ) g(u) = 0, \end{equation*} where $g(u)$ has superlinear growth at zero and sublinear…
Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent variables tend asymptotically to functions periodic with the…
For some planar Newtonian $N+3$-body problems, we use variational minimization methods to prove the existence of new periodic solutions satisfying that $N$ bodies chase each other on a curve, and the other 3 bodies chase each other on…
In dynamical systems theory, a fixed point of the dynamics is called nonhyperbolic if the linearization of the system around the fixed point has at least one eigenvalue with zero real part. The center manifold existence theorem guarantees…
We consider spin systems between a finite number $N$ of "species" or "phases" partitioning a cubic lattice $\mathbb{Z}^d$. We suppose that interactions between points of the same phase are coercive, while between point of different phases…
It is shown how to model any automorphism of a totally disconnected, locally compact group by a symbolic dynamical system. The model is an inverse limit of a product of a full-shift, on a finite number of symbols, with one of two types of…
Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density $\rho$ which either falls off at infinity or has compact support. The solutions have finite mass, finite…