arXiv subjects

Arpad Benyi

Publications and source records attributed to Arpad Benyi.

4 recordsLinked to original sources

arXiv2025

An elementary derivation of 3-cycles for a quadratic map

We present an elementary derivation of the period-three cycles for the real quadratic map $x\mapsto x^2+c$, a fundamental model in one-dimensional discrete dynamics. Using symmetric polynomials, we obtain a complete algebraic characterization of 3-cycles and determine explicit conditions for their existence and stability, without reliance on computer algebra. Through conjugacy with the logistic map, we recover the classical threshold values of the logistic parameter corresponding to the emergence and loss of stability of the 3-cycle. Our methodology outlines a transparent and algebraically grounded route to understanding the onset of chaos in quadratic and logistic dynamics.

math.DS↗

arXiv2012

A generalization of Routh's triangle theorem

We prove a generalization of the well known Routh's triangle theorem. As a consequence, we get a unification of the theorems of Ceva and Menelaus. A connection to Feynman's triangle is also given.

math.MG↗

arXiv2007

Modulation invariant bilinear T(1) theorem

We prove a T(1) theorem for bilinear singular integral operators (trilinear forms) with a one-dimensional modulation symmetry.

math.CA↗

arXiv2006

Unimodular Fourier multipliers for modulation spaces

We investigate the boundedness of unimodular Fourier multipliers on modulation spaces. Surprisingly, the multipliers with general symbol $e^{i|ξ|^α}$, where $α\in[0, 2]$, are bounded on all modulation spaces, but, in general, fail to be bounded on the usual $L^p$-spaces. As a consequence, the phase-space concentration of the solutions to the free Schrödinger and wave equations are preserved. As a byproduct, we also obtain boundedness results on modulation spaces for singular multipliers $|ξ|^{-δ} \sin (|ξ|^α)$ for $ 0 \leq δ\leq α$.

math.FA↗