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Each nowhere dense nonvoid closed set in Rn is a σ-limit set

Andrei Sivak (1996)

Fundamenta Mathematicae

We discuss main properties of the dynamics on minimal attraction centers (σ-limit sets) of single trajectories for continuous maps of a compact metric space into itself. We prove that each nowhere dense nonvoid closed set in ℝ n , n ≥ 1, is a σ-limit set for some continuous map.

Échanges de trois d'intervalles et suites sturmiennes

Gilles Didier (1997)

Journal de théorie des nombres de Bordeaux

On appelle échange d’intervalles l’application qui consiste à réordonner les intervalles d’une partition de [ 0 , 1 [ suivant une permutation donnée. Dans le cas des partitions en trois intervalles, nous donnons une caractérisation combinatoire des suites codant, d’après la partition définissant l’échange, l’orbite d’un point de [ 0 , 1 [ sous l’action de cette transformation.

Effective algebraic geometry and normal forms of reversible mappings.

Alain Jacquemard, Marco Antonio Teixeira (2002)

Revista Matemática Complutense

We present a new method to compute normal forms, applied to the germs of reversible mappings. We translate the classification problem of these germs to the theory of ideals in the space of the coefficients of their jets. Integral factorization coupled with Gröbner basis constructionjs the key factor that makes the process efficient. We also show that a language with typed objects like AXIOM is very convenient to solve these kinds of problems.

Effective equidistribution of S-integral points on symmetric varieties

Yves Benoist, Hee Oh (2012)

Annales de l’institut Fourier

Let K be a global field of characteristic not 2. Let Z = H ∖ G be a symmetric variety defined over K and S a finite set of places of K . We obtain counting and equidistribution results for the S-integral points of Z . Our results are effective when K is a number field.

Effective Hamiltonians and Quantum States

Lawrence C. Evans (2000/2001)

Séminaire Équations aux dérivées partielles

We recount here some preliminary attempts to devise quantum analogues of certain aspects of Mather’s theory of minimizing measures [M1-2, M-F], augmented by the PDE theory from Fathi [F1,2] and from [E-G1]. This earlier work provides us with a Lipschitz continuous function u solving the eikonal equation aėȧnd a probability measure σ solving a related transport equation.We present some elementary formal identities relating certain quantum states ψ and u , σ . We show also how to build out of u , σ an approximate...

Effects of competition and predation in a three species model

Janusz Szwabiński, Andrzej Pękalski, Kamil Trojan (2008)

Banach Center Publications

A model which consists of a predator and two prey species is presented. The prey compete for the same limited resource (food). The predator preys on both prey species but with different severity. We show that the coexistence of all three species is possible in a mean-field approach, whereas from Monte Carlo simulation it follows that the stochastic fluctuations drive one of the prey populations into extinction.

Efficiency analysis of control algorithms in spatially distributed systems with chaotic behavior

Łukasz Korus (2014)

International Journal of Applied Mathematics and Computer Science

The paper presents results of examination of control algorithms for the purpose of controlling chaos in spatially distributed systems like the coupled map lattice (CML). The mathematical definition of the CML, stability analysis as well as some basic results of numerical simulation exposing complex, spatiotemporal and chaotic behavior of the CML were already presented in another paper. The main purpose of this article is to compare the efficiency of controlling chaos by simple classical algorithms...

Eigenmodes of the damped wave equation and small hyperbolic subsets

Gabriel Rivière (2014)

Annales de l’institut Fourier

We study stationary solutions of the damped wave equation on a compact and smooth Riemannian manifold without boundary. In the high frequency limit, we prove that a sequence of β -damped stationary solutions cannot be completely concentrated in small neighborhoods of a small fixed hyperbolic subset made of β -damped trajectories of the geodesic flow.The article also includes an appendix (by S. Nonnenmacher and the author) where we establish the existence of an inverse logarithmic strip without eigenvalues...

Eigenvaluations

Charles Favre, Mattias Jonsson (2007)

Annales scientifiques de l'École Normale Supérieure

Eigenvalues and simplicity of interval exchange transformations

Sébastien Ferenczi, Luca Q. Zamboni (2011)

Annales scientifiques de l'École Normale Supérieure

For a class of d -interval exchange transformations, which we call the symmetric class, we define a new self-dual induction process in which the system is successively induced on a union of sub-intervals. This algorithm gives rise to an underlying graph structure which reflects the dynamical behavior of the system, through the Rokhlin towers of the induced maps. We apply it to build a wide assortment of explicit examples on four intervals having different dynamical properties: these include the first...

Eight-shaped Lissajous orbits in the Earth-Moon system

Grégory Archambeau, Philippe Augros, Emmanuel Trélat (2011)

MathematicS In Action

Euler and Lagrange proved the existence of five equilibrium points in the circular restricted three-body problem. These equilibrium points are known as the Lagrange points (Euler points or libration points) L 1 , ... , L 5 . The existence of families of periodic and quasi-periodic orbits around these points is well known (see [20, 21, 22, 23, 37]). Among them, halo orbits are 3-dimensional periodic orbits diffeomorphic to circles. They are the first kind of the so-called Lissajous orbits. To be selfcontained,...

EKF-based dual synchronization of chaotic colpitts circuit and Chua’s circuit

Shaohua Hong, Zhiguo Shi, Kangsheng Chen (2008)

Kybernetika

In this paper, dual synchronization of a hybrid system containing a chaotic Colpitts circuit and a Chua’s circuit, connected by an additive white Gaussian noise (AWGN) channel, is studied via numeric simulations. The extended Kalman filter (EKF) is employed as the response system to achieve the dual synchronization. Two methods are proposed and investigated. The first method treats the combination of a Colpitts circuit and a Chua’s circuit as a higher- dimensional system, while the second method...

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