Hyers-Ulam stability of elliptic Möbius difference equation

Abstract

The linear fractional map $f(z)=\frac{az+b}{cz+d}$ on the Riemann sphere with complex coefficients $ad-bc\ne 0$ is called Möbius map. If $f$ satisfies $ad-bc=1$ and $-2<a+d<2$, then $f$ is called $\text{elliptic}$ Möbius map. Let $\{b_n{\}}_{n\in {\mathbb{N}}_0}$ be the solution of the elliptic Möbius difference equation $b_{n+1}=f(b_n)$ for every $n\in {\mathbb{N}}_0$. Then the sequence $\{b_n{\}}_{n\in {\mathbb{N}}_0}$ has no Hyers-Ulam stability.

12 pages

References in corpus (10)

• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Fermi-liquid instabilities at magnetic quantum phase transitions
• Carrier transport in 2D graphene layers
• A self-consistent theory for graphene transport
• Why is the bulk resistivity of topological insulators so small?
• Gigantic negative magnetoresistance in a disordered topological insulator
• Revealing puddles of electrons and holes in compensated topological insulators
• Theory of the random potential and conductivity at the surface of a topological insulator
• Charge puddles in a completely compensated topological insulator
• Enhancement of hopping conductivity by spontaneous fractal ordering of low-energy sites

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• Charge puddles in the bulk and on the surface of the topological insulator BiSbTeSe${}_2$ studied by scanning tunneling microscopy and optical spectroscopy
• Quantum confinement of the Dirac surface states in topological-insulator nanowires
• Majorana bound states in topological insulators without a vortex
• Current-induced breakdown of the quantum anomalous Hall effect
• Tunable Coupling between Surface States of a Three-Dimensional Topological Insulator in the Quantum Hall Regime
• Conductivity of two-dimensional narrow gap semiconductors subjected to strong Coulomb disorder
• Metallization and proximity superconductivity in topological insulator nanowires
• Disorder effects in topological insulator nanowires
• Spatially varying electronic dephasing in three dimensional topological insulators
• Ionic and electronic properties of the topological insulator Bi${}_2$Te${}_2$Se investigated using $\beta$-detected nuclear magnetic relaxation and resonance of ${}^8$Li
• Conductivity of two-dimensional small gap semiconductors and topological insulators in strong Coulomb disorder
• Enhanced coherence and decoupled surface states in topological insulators through structural disorder
• Large positive magneto-conductivity at microwave frequencies in the compensated topological insulator BiSbTeSe2
• Nonlinear planar magnetotransport due to tilted Dirac cones in topological materials
• Characterizing the chemical potential disorder in the topological insulator (Bi${}_{1-x}$Sb${}_x$)${}_2$Te${}_3$ thin films
• Tracing Dirac points of topological surface states by ferromagnetic resonance
• Plasmons in semiconductor and topological insulator wires with large dielectric constant