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Benedict Irwin edited Difference Measure.tex
over 9 years ago
Commit id: b611f8cf06f5b701dc8b3d9ab5c1cffd1b0460f4
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diff --git a/Difference Measure.tex b/Difference Measure.tex
index f2d9cd4..0945479 100644
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So we may define the difference between two solutions as \begin{equation}
X(r)=\Bigg|\int_0^{m_1} r - \beta x \; \mathrm{dx} - \int_0^{m_2} r - \beta x \; \mathrm{dx}\Bigg|
\\
X(r)=| rm_1 - \frac{\beta m_1^2}{2} - rm_2 + \frac{\beta m_2^2}{2}|
\end{equation}
Think of labels, $\beta$ is inverse mass? $m$ is a $p$ then we have p^2/2m like kinetic and some perhaps potential like term.
This in theory should describe an asymmetric harmonic style oscillator potential?
Triangle Identity?
Norms?
Divided differences?
Counting function, bifurcations?
Series?
|m_1-m_2|=X(r), X(3)=0,
Some X_i(a_n)=0, may give solutions to bifurcation parameters...
There may be some grand width parameter $\Xi(r)$ which gives the largest to smallest bifurcation in the set, will be zero for single solution, X(r) for next etc. Determinants link?