Arithmetic Progressions and Chaos in Linear Dynamics
نویسندگان
چکیده
We characterize chaotic linear operators on reflexive Banach spaces in terms of the existence long arithmetic progressions sets return times. also show that this characterization does not hold for arbitrary spaces. To achieve this, we study $$\mathcal {F}$$ -hypercyclicity a family subsets natural numbers associated to arbitrarily progressions.
منابع مشابه
Primes in arithmetic progressions
Strengthening work of Rosser, Schoenfeld, and McCurley, we establish explicit Chebyshev-type estimates in the prime number theorem for arithmetic progressions, for all moduli k ≤ 72 and other small moduli.
متن کاملDiscrepancy in Arithmetic Progressions
It is proven that there is a two-coloring of the first n integers forwhich all arithmetic progressions have discrepancy less than const.n1/4. Thisshows that a 1964 result of K. F. Roth is, up to constants, best possible. Department of Applied Mathematics, Charles University, Malostranské nám. 25,118 00 Praha 1, Czech RepublicE-mail address: [email protected] Courant Insti...
متن کاملOn rainbow 4-term arithmetic progressions
{sl Let $[n]={1,dots, n}$ be colored in $k$ colors. A rainbow AP$(k)$ in $[n]$ is a $k$ term arithmetic progression whose elements have different colors. Conlon, Jungi'{c} and Radoiv{c}i'{c} cite{conlon} prove that there exists an equinumerous 4-coloring of $[4n]$ which is rainbow AP(4) free, when $n$ is even. Based on their construction, we show that such a coloring of $[4n]$...
متن کاملPrimes in arithmetic progressions
[1] Euler’s proof uses only simple properties of ζ(s), and only of ζ(s) as a function of a real, rather than complex, variable. Given the status of complex number and complex analysis in Euler’s time, this is not surprising. It is slightly more surprising that Dirichlet’s original argument also was a real-variable argument, since by that time, a hundred years later, complex analysis was well-es...
متن کاملArithmetic Progressions on Conics.
In this paper, we look at long arithmetic progressions on conics. By an arithmetic progression on a curve, we mean the existence of rational points on the curve whose x-coordinates are in arithmetic progression. We revisit arithmetic progressions on the unit circle, constructing 3-term progressions of points in the first quadrant containing an arbitrary rational point on the unit circle. We als...
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: Integral Equations and Operator Theory
سال: 2022
ISSN: ['0378-620X', '1420-8989']
DOI: https://doi.org/10.1007/s00020-022-02687-3