Related papers: Periodic behaviors
We develop a new theory of maximizing sets in dynamical systems, for the study of ergodic optimization in systems with weak hyperbolicity but where the Ma\~n\'e cohomology lemma does not hold. This leads to new solutions of the Typical…
A subset X of a vector space V is said to have the "Separation Property" if it separates linear forms in the following sense: given a pair (a, b) of linearly independent forms on V there is a point x on X such that a(x)=0 and b(x) is not…
Dynamical system properties give rise to effects in Statistical Mechanics. Topological index changes can be the basis for phase transitions. The Euler characteristic is a versatile topological invariant that can be evaluated for model…
We show that for certain classes of actions of Z^d, d >= 2, by automorphisms of the torus any measurable conjugacy has to be affine, hence measurable conjugacy implies algebraic conjugacy; similarly any measurable factor is algebraic, and…
The long-time behavior is one of the most fundamental properties of dynamical systems. Poincar\'e studied the Poisson stability to capture the property of whether points return arbitrarily near the initial positions. Birkhoff studied the…
This work represents an in-depth study of the structural behavior of the Collatz sequences. We consider a finite arithmetic progression with a common difference is 2 and the number of terms in the sequence is equal to 2^n . After, we…
The purpose of this note is to give an exposition of some interesting combinatorics and convex geometry concepts that appear in algebraic geometry in relation to counting the number of solutions of a system of polynomial equations in…
This survey article is the outgrowth of two talks given at the Journ\'ees X-UPS "P\'eriodes et transcendance" at \'Ecole polytechnique. Periods are complex numbers whose real and imaginary parts can be written as integrals of rational…
Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…
We give some characterizations for the critical values at infinity of a rational function in two complex variables in terms of the Euler characteristic, the Malgrange condition and the M-tameness
We analyse the dynamics of an array of $N^2$ identical cells coupled in the shape of a torus. Each cell is a 2-dimensional ordinary differential equation of FitzHugh-Nagumo type and the total system is…
We consider functions which are subfunctions with respect to the differential operator $$L_\rho = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + 2\rho \frac{\partial}{\partial x} + \rho^2 $$ and are doubly periodic in…
The aim of this paper is to investigate the boundedness of periodic Fourier integral operators in Lebesgue spaces with variable exponent $L^{p(\cdot)}$ on the $n$-dimensional torus. We deal with operators of type $(\rho, \delta)$ which…
Bloch theorem for a periodic operator is being revisited here, and we notice extra orthogonality relationships. It is shown that solutions are bi-periodic, in the sense that eigenfunctions are periodic with respect to one argument, and…
Using abelian differentials and periods of the universal Mumford curve, we study the universal expression and asymptotic behavior of tau functions defined for stably degenerating families of algebraic curves with additional data.…
We consider the rotation set $\rho(F)$ for a lift $F$ of an area preserving homeomorphism $f: \t^2\to \t^2$, which is homotopic to the identity. The relationship between this set and the existence of periodic points for $f$ is least well…
We study the functional considered in~\cite{2011PhRvB..84f4205G,2014CMaPh.tmp..127G,GiuSeirGS} and a continuous version of it, analogous to the one considered in~\cite{GR}. The functionals consist of a perimeter term and a non-local term…
This paper announces results on the behavior of some important algebraic and topological invariants --- Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. --- and their associated…
Several classes of tempered measures are characterised that are eigenmeasures of the Fourier transform, the latter viewed as a linear operator on (generally unbounded) Radon measures on $\RR^d$. In particular, we classify all periodic…
Complex projective algebraic varieties with $\mathbb{C}^*$-actions can be thought of as geometric counterparts of birational transformations. In this paper we describe geometrically the birational transformations associated to rational…