Related papers: Arithmetic and growth of periodic orbits
Piecewise smooth maps are known to exhibit a wide range of dynamical features including numerous types of periodic orbits. Predicting regions in parameter space where such periodic orbits might occur and determining their stability is…
We present an illustrative application of the two famous mathematical theorems in differential topology in order to show the existence of periodic orbits with arbitrary given period for a class of hamiltonians .This result point out for a…
We will show that if a dynamical system has enough constants of motion then a Moser-Weinstein type theorem can be applied for proving the existence of periodic orbits in the case when the linearized system is degenerate.
We investigate global continuation of periodic orbits of a differential equation depending on a parameter, assuming that a closed 1-form satisfying certain properties exists. We begin by extending the global continuation theory of…
In this work the existence of periodic solutions is studied for the Hamiltonian functions (Formula presented.) where the first term consist of a harmonic oscillator and the second term are homogeneous polynomials of degree 5 defined by two…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
Given an integer $n$, we introduce the integral Lie ring of partitions with bounded maximal part, whose elements are in one-to-one correspondence to integer partitions with parts in $\{1,2,\dots, n-1\}$. Starting from an abelian subring, we…
Mathematical billiards is much like the real game: a point mass, representing the ball, rolls in a straight line on a (perfectly friction-less) table, striking the sides according to the law of reflection. A billiard trajectory is then…
Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…
In this work, we study the continuation of a periodic orbit on a relatively large scale and discover the existence of convergence under certain conditions, which has profound significance in research on asteroids and can provide a total…
In this note, we consider the problem of choosing which nodes of a linear dynamical system should be actuated so that the state transfer from the system's initial condition to a given final state is possible. Assuming a standard complexity…
We prove a special case of a dynamical analogue of the classical Mordell-Lang conjecture. In particular, let $\phi$ be a rational function with no superattracting periodic points other than exceptional points. If the coefficients of $\phi$…
Uncovering the formation process that reproduces the distinct properties of compact super-Earth exoplanet systems is a major goal of planet formation theory. The most successful model argues that non-resonant systems begin as resonant…
The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions…
For polynomials and rational maps of fixed degree over a finite field, we bound both the average number of connected components of their functional graphs as well as the average number of periodic points of their associated dynamical…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single valued integrals of motion each. All…
An integer sequence is called realizable if it is the count of periodic points of some map. The Fibonacci sequence $(F_n)$ does not have this property, and the Fibonacci sequence sampled along the squares $(F_{n^2})$ also does not have this…
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…