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2012, Volume 1
A Quantitative Reasoning Framework and the Importance of Quantitative Modeling in Biology
Bifurcations and Dynamical Behavior of 2D Coupled Chaotic Sine Maps
Discrete Probability of Random Möbius Groups: Random Subgroups by Two Generators
be real Möbius groups. For any 2×2 matrix A in induces real Möbius transformations g by the formula 
where 
. The collection of all real Möbius transformations for which 
takes the values 1 forms a group which can be identified with 
. We write 
to mean that f is a random variable in. In this paper, we study the random Möbius subgroup
. We can g...
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, the probability 
is greater than 0.027282. (2) If f is hyperbolic transformation and g is parabolic transformation, then the probability 
is discrete is greater than 7/12. (3) If f is elliptic of order n and g is elliptic of order 2, then the probability