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A new proof of a conjecture of Yoccoz

Xavier Buff, Arnaud Chéritat (2011)

Annales de l’institut Fourier

We give a new proof of the following conjecture of Yoccoz: ( ∃ C ∈ ℝ ) ( ∀ θ ∈ ℝ ∖ ℚ ) log rad Δ ( Q θ ) ≤ - Y ( θ ) + C , where Q θ ( z ) = e 2 π i θ z + z 2 , Δ ( Q θ ) is its Siegel disk if Q θ is linearizable (or ∅ otherwise), rad Δ ( Q θ ) is the conformal radius of the Siegel disk of Q θ (or 0 if there is none) and Y ( θ ) is Yoccoz’s Brjuno function.In a former article we obtained a first proof based on the control of parabolic explosion. Here, we present a more elementary proof based on Yoccoz’s initial methods.We then extend this result to some new families of polynomials such as z d + c with d > 2 . We also show that...

A non-linear discrete-time dynamical system related to epidemic SISI model

Sobirjon K. Shoyimardonov (2021)

Communications in Mathematics

We consider SISI epidemic model with discrete-time. The crucial point of this model is that an individual can be infected twice. This non-linear evolution operator depends on seven parameters and we assume that the population size under consideration is constant, so death rate is the same with birth rate per unit time. Reducing to quadratic stochastic operator (QSO) we study the dynamical system of the SISI model.

A note on a conjecture of Duval and sturmian words

Filippo Mignosi, Luca Q. Zamboni (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We prove a long standing conjecture of Duval in the special case of sturmian words.

A note on a generalization of Diliberto's Theorem for certain differential equations of higher dimension

Ladislav Adamec (2005)

Applications of Mathematics

In the theory of autonomous perturbations of periodic solutions of ordinary differential equations the method of the Poincaré mapping has been widely used. For the analysis of properties of this mapping in the case of two-dimensional systems, a result first obtained probably by Diliberto in 1950 is sometimes used. In the paper, this result is (partially) extended to a certain class of autonomous ordinary differential equations of higher dimension.

A note on a generalized cohomology equation

K. Krzyżewski (2000)

Colloquium Mathematicae

We give a necessary and sufficient condition for the solvability of a generalized cohomology equation, for an ergodic endomorphism of a probability measure space, in the space of measurable complex functions. This generalizes a result obtained in [7].

A Note on an Application of the Lasota-York Fixed Point Theorem in the Turbulent Transport Problem

Tomasz Komorowski, Grzegorz Krupa (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

We study a model of motion of a passive tracer particle in a turbulent flow that is strongly mixing in time variable. In [8] we have shown that there exists a probability measure equivalent to the underlying physical probability under which the quasi-Lagrangian velocity process, i.e. the velocity of the flow observed from the vintage point of the moving particle, is stationary and ergodic. As a consequence, we proved the existence of the mean of the quasi-Lagrangian velocity, the so-called Stokes...

A note on generic chaos

Gongfu Liao (1994)

Annales Polonici Mathematici

We consider dynamical systems on a separable metric space containing at least two points. It is proved that weak topological mixing implies generic chaos, but the converse is false. As an application, some results of Piórek are simply reproved.

A note on LaSalle's problems

Anna Cima, Armengol Gasull, Francesc Mañosas (2001)

Annales Polonici Mathematici

In LaSalle's book "The Stability of Dynamical Systems", the author gives four conditions which imply that the origin of a discrete dynamical system defined on ℝ is a global attractor, and proposes to study the natural extensions of these conditions in ℝⁿ. Although some partial results are obtained in previous papers, as far as we know, the problem is not completely settled. In this work we first study the four conditions and prove that just one of them implies that the origin is a global attractor...

A note on M. Soares’ bounds

Eduardo Esteves, Israel Vainsencher (2006)

Annales de l’institut Fourier

We give an intersection theoretic proof of M. Soares’ bounds for the Poincaré-Hopf index of an isolated singularity of a foliation of ℂℙ n .

Currently displaying 161 – 180 of 4754