Advanced Differential Equations and Dynamical Systems

This article studies approximations to the set of trajectories, attainable sets and integral funnel of a control system described by an ordinary differential equation. It is assumed that the equation is nonlinear with respect to the phase state vector and affine with respect to the control vector. The system includes…

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Let $f:\mathbb{P}^1\to\mathbb{P}^1$ be a quadratic rational map defined over the rational field $\mathbb{Q}$ with nonabelian automorphism group. We prove that no such map has a $\mathbb{Q}$-rational periodic point with exact period $N\ge 4$. We also give an explicit parametrization of such maps that have $\mathbb{Q}$-…

Let $f:\mathbb{P}^1\to\mathbb{P}^1$ be a quadratic rational map defined over the rational field $\mathbb{Q}$ with nonabelian automorphism group. We prove that no such map has a $\mathbb{Q}$-rational periodic point with exact period $N\ge 4$. We also give an explicit parametrization of such maps that have $\mathbb{Q}$-…

ABSTRACT It was conjectured by Flynn that there exists a constant such that, for any integer , any , there exists a hyperelliptic curve of genus over with a rational ‐torsion point on its Jacobian. Leprévost proved this conjecture with . In this work, we prove that given an integer in the interval , , satisfying certa…

This study is devoted to dynamical analysis of following higher order difference equation \begin{eqnarray*}x_{n+1}=px_{n}+\frac{q}{rx_{n-k}^{2}},k\in \{1,2,...\}, \end{eqnarray*} where $p, q, r$ and the initial conditions are positive real numbers. In particular, we discuss the existence of periodic solutions of the d…

Abstract. We show that in the periodic homogenization of uniformly elliptic Hamilton–Jacobi equations with quasiconvex Hamiltonians in arbitrary dimensions, the effective Hamiltonian is not necessarily quasiconvex. This observation is in sharp contrast with the first-order case, where homogenization is known to preser…

We investigate localization in a one-dimensional quasiperiodic lattice obtained by extending the Aubry-André model with a structured N th -neighbor hopping term of strength J N . This additional channel connects successive windings of an effective helical chain, introducing both a hopping scale and a geometric length…

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We study modular polynomial invariants of the cyclic group $C_p$ over a field of characteristic $p$ where $p$ is a prime number and use the reverse lexicographic order. We focus on the leading monomial of an invariant by considering the degrees of the terminal variables. It is obtained that this degree of each termina…

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• GÜNAY ASLAN

This paper investigates the qualitative behavior, global dynamics, and explicit solution forms of four distinct coupled systems of third-order rational difference equations. By employing an analytical approach based on mathematical induction and recursive substitution, we derive the general closed-form expressions for…

• BURAK OĞUL