On the multiplier of a repelling fixed point

1994 ◽  
Vol 118 (1) ◽  
pp. 85-108 ◽  
Author(s):  
Lisa R. Goldberg
Keyword(s):  
Fixed Point ◽  
Repelling Fixed Point

scholarly journals Hyers-Ulam stability of hyperbolic Möbius difference equation

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4555-4575 ◽  
Author(s):  
Young Nam
Keyword(s):  
Fixed Point ◽  
Difference Equation ◽  
Line Segment ◽  
Initial Point ◽  
Logistic Equation ◽  
Complex Numbers ◽  
Ulam Stability ◽  
The Difference ◽  
The Stability ◽  
Repelling Fixed Point

Hyers-Ulam stability of the difference equation with the initial point z0 as follows zi+1 = azi+b/czi+d is investigated for complex numbers a,b,c and d where ad-bc = 1, c ? 0 and a+d ?R\[-2,2]. The stability of the sequence {zn}n?N0 holds if the initial point is in the exterior of a certain disk of which center is ?d/c . Furthermore, the region for stability can be extended to the complement of some neighborhood of the line segment between -d/c and the repelling fixed point of the map z ? az+b/cz+d. This result is the generalization of Hyers-Ulam stability of Pielou logistic equation.

scholarly journals Outer compositions of hyperbolic/loxodromic linear fractional transfomations

1992 ◽  
Vol 15 (4) ◽  
pp. 819-822 ◽  
Author(s):  
John Gill
Keyword(s):  
Fixed Point ◽  
Continued Fractions ◽  
Analytic Theory ◽  
Complex Numbers ◽  
Linear Fractional Transformations ◽  
Classical Means ◽  
Repelling Fixed Point ◽  
Attracting Fixed Point

It is shown, using classical means, that the outer composition of hyperbolic or loxodromic linear fractional transformations{fn}, wherefn→f, converges toα, the attracting fixed point off, for all complex numbersz, with one possible exception,z0. I.e.,Fn(z):=fn∘fn−1∘…∘f1(z)→αWhenz0exists,Fn(z0)→β, the repelling fixed point off. Applications include the analytic theory of reverse continued fractions.

Contracting on Average Random IFS with Repelling Fixed Point

2006 ◽  
Vol 122 (1) ◽  
pp. 169-193 ◽  
Author(s):  
Ai Hua Fan ◽  
Károly Simon ◽  
Hajnal R. Tóth
Keyword(s):  
Fixed Point ◽  
Repelling Fixed Point

Mental equilibrium: Identifying fixed-point attractors in the stream of thought

2003 ◽  
Author(s):  
Robin R. Vallacher ◽  
Andrzej Nowak ◽  
Matthew Rockloff
Keyword(s):  
Fixed Point

Bifurcation in a Simple Model of the Cardiovascular System

2000 ◽  
Vol 39 (02) ◽  
pp. 118-121 ◽  
Author(s):  
S. Akselrod ◽  
S. Eyal
Keyword(s):  
Nonlinear Dynamics ◽  
Blood Pressure ◽  
Heart Rate ◽  
Fixed Point ◽  
Cardiovascular System ◽  
Modified Model ◽  
Mayer Waves ◽  
Sustained Oscillations ◽  
Human Cardiovascular System ◽  
Physiological Values

Abstract:A simple nonlinear beat-to-beat model of the human cardiovascular system has been studied. The model, introduced by DeBoer et al. was a simplified linearized version. We present a modified model which allows to investigate the nonlinear dynamics of the cardiovascular system. We found that an increase in the -sympathetic gain, via a Hopf bifurcation, leads to sustained oscillations both in heart rate and blood pressure variables at about 0.1 Hz (Mayer waves). Similar oscillations were observed when increasing the -sympathetic gain or decreasing the vagal gain. Further changes of the gains, even beyond reasonable physiological values, did not reveal another bifurcation. The dynamics observed were thus either fixed point or limit cycle. Introducing respiration into the model showed entrainment between the respiration frequency and the Mayer waves.

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion
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