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contenido/transformaciones_lineales_fraccionarias.html

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@@ -528,13 +528,14 @@ <h3>3. Clasificación mediante la traza</h3>
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<p>
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Dado que multiplicar la matriz por un escalar no nulo no cambia la transformación de Möbius,
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podemos <strong>normalizar</strong> la matriz para que su determinante sea igual a $1$
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(es decir, trabajar con $SL(2,\mathbb{C})$, el grupo lineal especial). Después de esta normalización, la clasificación
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(es decir, trabajar con $SL(2,\mathbb{C})$, el
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<a href="https://es.wikipedia.org/wiki/Grupo_lineal_especial">grupo lineal especial</a>). Después de esta normalización, la clasificación
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depende del valor de la traza $\tau = a + d$:
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</p>
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<ul>
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<li>
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<strong>Elíptica:</strong> $\tau \in \mathbb{R}$ y $|\tau| < 2$. </li>
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<strong>Elíptica:</strong> $\tau \in \mathbb{R}$ y $|\tau| \lt 2$. </li>
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<li>
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<strong>Parabólica:</strong> $\tau = \pm 2$ (el punto fijo es único).
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</li>

content/linear_fractional_transformations.html

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@@ -524,13 +524,14 @@ <h3>3. Classification using the trace</h3>
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<p>
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Since multiplying the matrix by a nonzero scalar does not change the Möbius transformation,
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we can <strong>normalize</strong> the matrix so that its determinant equals $1$
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(i.e., work with $SL(2,\mathbb{C})$, the linear special group). After this normalization, the classification
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(i.e., work with $SL(2,\mathbb{C})$,
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the <a href="https://en.wikipedia.org/wiki/Special_linear_group" target="_blank">special linear group</a>). After this normalization, the classification
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depends on the value of the trace $\tau = a + d$:
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</p>
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<ul>
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<li>
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<strong>Elliptic:</strong> $\tau \in \mathbb{R}$ and $|\tau| < 2$. </li>
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<strong>Elliptic:</strong> $\tau \in \mathbb{R}$ and $|\tau| \lt 2.$ </li>
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<li>
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<strong>Parabolic:</strong> $\tau = \pm 2$ (the fixed point is unique).
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</li>

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