¥¢) Properties of Möbius Transformations
¨ç All Möbius Transformations are bijective mapping.
¨è All Möbius Transformations are analytic in a domain D.
¨é (where a, b, c, d are complex number)¿¡ ´ëÇÏ¿© ad-bc¡Á0ÀÌ´Ù.
¸¸¾à ad-bc¡Á0À̸é À̹ǷΠ»ó¼ö°¡ µÈ´Ù. µû¶ó¼ ÀÌ°ÍÀº ¿ì¸®°¡ ¿øÇÏ´Â °ÍÀÌ ¾Æ´Ï¹Ç·Î ad-bc¡Á0ÀÎ °æ¿ì¸¦ Á¦¿ÜÇÏ¿©¾ß ÇÑ´Ù.
¨ê ÀÓÀÇÀÇ Möbius TransformationsÀº Rotation, Reflection, magnification, Translation°ú inversionÀÇ ÇÕ¼ºÇÔ¼ö·Î Ç¥Çö µÉ ¼ö ÀÖ´Ù.
(where a, b, c, d are complex number)À̸é
Figure. 7.22ÀÌ°í ÀÌ°ÍÀº ´ÙÀ½°ú °°ÀÌ ³ª´ ¼ö ÀÖ´Ù.
¤¡) : translation
¤¤) : inversion
¤§) : magnification & rotation
¤©) : translation
3. ¹®Á¦¿¡ Àû¿ë
Exercise 7.3ÀÇ ¹®Á¦ 12¹ø
`12. Find Möbius Transformations that takes the half plane depicted in Fig .7.22 onto the unit disk `
¹®Á¦ Ç®ÀÌÀÇ Âø¾ÈÀº ´ÙÀ½°ú °°´Ù. ¸ÕÀú ¹®Á¦ÀÇ ¿µ¿ªÀ» ±×¸²À¸·Î Ç¥½ÃÇÑ ÈÄ¡¦(»ý·«)
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