Dosiero:J-inv-poincare.jpeg

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Klein's J-invariant, modulus on Poincare disk (600x600 pixels)

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[redaktu] Detailed description

This image shows the modulus | j | of the J-invariant j=g_2^3/\Delta as a function on the Poincare disk. The Poincare disk is a mapping of the upper half-plane to the the unit disk by means of the Mobius transformation

z=\frac{\tau-i}{\tau+i}

where τ is the half-period ratio, that is, the coordinate on the upper half-plane. The left-right symmetry of this image corresponds to the \tau\to -1/\tau symmetry of the J-invariant, as small values for the imaginary part of τ are mapped to z=−1 on the left hand side, while large values for the imaginary part of τ are mapped to z=+1 on the right side. The fundamental domain is a triangle spanning the two vertically oriented dots in the center, with the cusp at z=+1 on the right. The transformation \tau\to\tau+1 corresponds to walking the fundamental domain from dot to dot on the boundary of the largest red area on the right; the cusp z=+1 remains unchanged.

For a detailed description of other aspects of this picture, including the coloration, please refer to Image:J-inv-modulus.jpeg.

It, and other related images, can be seen at http://www.linas.org/art-gallery/numberetic/numberetic.html

[redaktu] Source of Image

Created by Linas Vepstas User:Linas <linas@linas.org> on 21 May 2005 using custom software written entirely by Linas Vepstas.

[redaktu] Copyright status

Released under the Gnu Free Documentation License (GFDL) by Linas Vepstas.

Permeso estas donita kopii, distribui kaj/aŭ modifi tiun ĉi verkon sub la kondiĉoj de la GNU Free Documentation License, Versio 1.2 aŭ ia ajn alia versio eldonita de la Free Software Foundation; kun neniaj Senvariaj Sekcioj, neniaj Antaŭ-Kovrilaj Tekstoj, kaj neniaj Malantaŭ-Kovrilaj Tekstoj.
Kondiĉe de malgarantioj.

[redaktu] Relevant Links

  • Weierstrass elliptic functions
  • Eisenstein series
  • Q-series
date/time username edit summary
02:37, 23 May 2005 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:J-inv-poincare.jpeg#Detailed_description" title="Image:J-inv-poincare.jpeg">→</a>Detailed description -</span> tweak)
02:34, 23 May 2005 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:J-inv-poincare.jpeg#Detailed_description" title="Image:J-inv-poincare.jpeg">→</a>Detailed description -</span>add clarifying text)
01:40, 22 May 2005 en:User:Linas (provide image details)
01:30, 22 May 2005 en:User:Linas (Klein's J-invariant, modulus on Poincare disk (600x600 pixels) )

[redaktu] Historio de la dosiero

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  • (del) (cur) 01:30, 22 May 2005 . . en:User:Linas Linas ( en:User_talk:Linas Talk) . . 600x600 (38354 bytes) (Klein's J-invariant, modulus on Poincare disk (600x600 pixels) )

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Dato/HoroUzuloGrandecojDosiergrandecoKomento
(nun)20:39, 19. Mar 2006Maksim-bot (Diskuto | kontribuoj)600×60037 KBLa bildo estas kopiita de wikipedia:en. La originala priskribo estas: Klein's J-invariant, modulus on Poincare disk (600x600 pixels) ===Detailed description=== This image shows the modulus <math>|j|</math> of the J-invariant <math>j=g_2^3/\Delta</ma

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