Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics
نویسندگان
چکیده
منابع مشابه
Recurrence Plots for Symbolic Sequences
This paper introduces an extension of recurrence analysis to symbolic sequences. Heuristic arguments based on Shannon-McMillan-Breiman theorem suggest several relations between the statistical features of ‘symbolic’ recurrence plots and the entropy per unit time of the dynamics; their practical efficiency for experimental sequences of finite length is checked numerically on two paradigmatic mod...
متن کاملRotation Sets and Almost Periodic Sequences
We study the rotational behaviour on minimal sets of torus homeomorphisms and show that the associated rotation sets can be any type of line segments as well as non-convex and even plane-separating continua. This shows that restrictions which hold for rotation set on the whole torus are not valid on minimal sets. The proof uses a construction of rotational horseshoes by Kwapisz to transfer the ...
متن کاملEfficiently determining Convergence in Polynomial Recurrence Sequences
We derive the necessary and sufficient condition, for a given Polynomial Recurrence Sequence to converge to a given target rational K. By converge, we mean that the Nth term of the sequence, is equal to K, as N tends to positive infinity. The basic idea of our approach is to construct a univariate polynomial equation in x, whose coefficients correspond to the terms of the Sequence. The approa...
متن کاملPolynomial and Linearized Normal Forms for Almost Periodic Differential Systems
For almost periodic differential systems ẋ = εf(x, t, ε) with x ∈ Cn, t ∈ R and ε > 0 small enough, we get a polynomial normal form in a neighborhood of a hyperbolic singular point of the system ẋ = ε limT→∞ 1 T ∫ T 0 f(x, t, 0) dt, if its eigenvalues are in the Poincaré domain. The normal form linearizes if the real part of the eigenvalues are non–resonant.
متن کاملDynamics of Almost Periodic Scalar Parabolic Equations
The current paper is devoted to study of the asymptotic behavior of bounded solutions for the following type of parabolic equation: u t = u xx + f (t, x, u, u x), t > 0, 0 < x < 1, (1.1) with the boundary conditions: βu(t, 0) + (1 − β)u x (t, 0) = 0, βu(t, 1) + (1 − β)u x (t, 1) = 0, t > 0, (1.2) where β = 0 or 1, f : IR 1 × [0, 1] × IR 1 × IR 1 → IR 1 is C 2 , and f (t, x, u, p) with all its p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2018
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2017.130