Timeline for Convergence of Affine Transformations
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Oct 23, 2009 at 12:35 | vote | accept | streklin | ||
| Oct 23, 2009 at 0:55 | answer | added | Marko Budisic | timeline score: 1 | |
| Oct 16, 2009 at 17:16 | history | edited | streklin | CC BY-SA 2.5 |
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| Oct 16, 2009 at 16:37 | history | edited | streklin | CC BY-SA 2.5 |
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| Oct 16, 2009 at 12:41 | comment | added | streklin | Well I am not entirely sure what I am looking for yet, but I do see your point. I am pretty sure I can derive some constraints for which the things converge and a_ix + b_i don't all have a_i = 1 or b_i = 0 - but I am sure other questions could be asked i.e. Is there a subgroup which any members will converge in this fashion when iterated? Are there non-obvious conditions for convergence? Is there anything about what happens to the image of such transforms in general? Can I have a puppy? :) I am working on narrowing down what I need, but at the moment I am collecting puzzle pieces. | |
| Oct 16, 2009 at 5:34 | comment | added | David E Speyer | Could you give us some more clues as to what you're looking for. Any convergent sum is an example of this phenomenon (since x --> x+a_i is an affine map, the sum \sigma a_i converges if and only if the corresponding sequence of translations does.) Similarly, any infinite product is an example. | |
| Oct 16, 2009 at 2:03 | history | asked | streklin | CC BY-SA 2.5 |