Möbius Transformations on ℝn

Ordinary differential equations invariant under two-variable Möbius transformations

Applied Mathematics Letters ◽

10.1016/j.aml.2021.107105 ◽

2021 ◽

Vol 117 ◽

pp. 107105

Author(s):

M. Euler ◽

N. Euler ◽

M.C. Nucci

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Möbius Transformations ◽

Mobius Transformations

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Corrigendum to “A new characteristic of Möbius transformations in hyperbolic geometry” [J. Math. Anal. Appl. 319 (2) (2006) 660–664]

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2010.11.057 ◽

2011 ◽

Vol 376 (1) ◽

pp. 383-384 ◽

Cited By ~ 2

Author(s):

Shihai Yang ◽

Ainong Fang

Keyword(s):

Hyperbolic Geometry ◽

Möbius Transformations ◽

Mobius Transformations

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Möbius Transformations and Periodic Solutions of Complex Riccati Equations

Bulletin of the London Mathematical Society ◽

10.1112/s0024609396002160 ◽

1997 ◽

Vol 29 (2) ◽

pp. 205-215 ◽

Cited By ~ 19

Author(s):

Juan Campos

Keyword(s):

Periodic Solutions ◽

Riccati Equations ◽

Möbius Transformations ◽

Mobius Transformations

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Möbius geometry for hypersurfaces in S4

Nagoya Mathematical Journal ◽

10.1017/s0027763000005274 ◽

1995 ◽

Vol 139 ◽

pp. 1-20 ◽

Cited By ~ 16

Author(s):

Changping Wang

Keyword(s):

Invariant System ◽

Principal Curvatures ◽

Möbius Transformations ◽

Möbius Geometry ◽

Mobius Transformations

Our purpose in this paper is to study Möbius geometry for those hypersurfaces in S4 which have different principal curvatures at each point. We will give a complete local Möbius invariant system for such hypersurface in S4 which determines the hypersurface up to Möbius transformations. And we will classify the so-called Möbius homogeneous hypersurfaces in S4.

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MÖBIUS TRANSFORMATIONS IN QUANTUM AMPLITUDE AMPLIFICATION WITH GENERALIZED PHASES

International Journal of Quantum Information ◽

10.1142/s0219749910005764 ◽

2010 ◽

Vol 08 (06) ◽

pp. 923-935 ◽

Cited By ~ 1

Author(s):

CÉSAR BAUTISTA-RAMOS ◽

NORA CASTILLO-TÉPOX

Keyword(s):

Error Probability ◽

Quantum Algorithm ◽

Linear Transformations ◽

Möbius Transformations ◽

Good State ◽

Quantum Amplitude ◽

Initial States ◽

Phase Angles ◽

Amplitude Amplification ◽

Mobius Transformations

The iteration of the operators employed in quantum amplitude amplification with generalized phases is analyzed by using elementary properties (geometric and algebraic) of the Möbius transformations (fractional linear transformations). It is shown that, for a given quantum algorithm without measurement, which produces a good state with probability a of success, if the phase angles φ and ϕ which mark the good and initial states respectively satisfy φ = ϕ with a small enough, then, for a number n of iterations with [Formula: see text] we get an error probability that is at most O(aϕ2).

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