A QRT-System of Two Order One Homographic Difference Equations: Conjugation to Rotations, Periods of Periodic Solutions, Sensitiveness to Initial Conditions

DOI10.1007/978-3-662-52927-0_18zbMath1355.39014arXiv1407.0918OpenAlexW136594287MaRDI QIDQ2954216

Marc Rogalski, Guy Bastien

Publication date: 12 January 2017

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.0918

zbMATH Keywords

periodic solutionsdynamical systemchaotic behaviorrational difference equationsminimal periodsensitiveness to initial conditions

Mathematics Subject Classification ID

Multiplicative and other generalized difference equations (39A20) Periodic solutions of difference equations (39A23) Chaotic behavior of solutions of difference equations (39A33)

Related Items (4)

Unnamed Item ⋮ The periodic orbits of a dynamical system associated with a family of QRT-maps ⋮ QRT-families of degree four biquadratic curves each of them has genus zero, associated dynamical systems ⋮ Unnamed Item

Cites Work

• On some algebraic difference equations \(u_{n+2} u_{n}= \psi(u_{n+1})\) in \(\mathbb R_*^+\), related to families of conics or cubics: generalization of the Lyness' sequences
• On the algebraic difference equations \(u_{n+2}+u_{n}=\psi (u_{n+1})\) in \(\mathbb R\), related to a family of elliptic quartics in the plane
• Integrable mappings and soliton equations
• Level sets lemmas and unicity of critical point of invariants, tools for local stability and topological properties of dynamical systems
• Estimation de la fonction de Tchebychef θ sur le k-ième nombre premier et grandes valeurs de la fonction ω(n) nombre de diviseurs premiers de n
• Global Behavior of the Solutions of Lyness' Difference Equation
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