Outer compositions of hyperbolic/loxodromic linear fractional transfomations
It is shown, using classical means, that the outer composition of hyperbolic or loxodromic linear fractional transformations {fn}, where fn→f, converges to α, the attracting fixed point of f, for all complex numbers z, with one possible exception, z0. I.e.,Fn(z):=fn∘fn−1∘…∘f1(z)→αWhen z0 exists, Fn(...
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| Format: | Article |
| Language: | English |
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Wiley
1992-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117129200108X |
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| _version_ | 1850218453611315200 |
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| author | John Gill |
| author_facet | John Gill |
| author_sort | John Gill |
| collection | DOAJ |
| description | It is shown, using classical means, that the outer composition of hyperbolic or loxodromic linear fractional transformations {fn}, where fn→f, converges to α, the attracting fixed point of f, for all complex numbers z, with one possible exception, z0. I.e.,Fn(z):=fn∘fn−1∘…∘f1(z)→αWhen z0 exists, Fn(z0)→β, the repelling fixed point of f. Applications include the analytic theory of reverse continued fractions. |
| format | Article |
| id | doaj-art-370796927af14d15803143473cb0871c |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1992-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-370796927af14d15803143473cb0871c2025-08-20T02:07:45ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115481982210.1155/S016117129200108XOuter compositions of hyperbolic/loxodromic linear fractional transfomationsJohn Gill0Mathematics Department, University of Southern Colorado, Pueblo, CO 81001, USAIt is shown, using classical means, that the outer composition of hyperbolic or loxodromic linear fractional transformations {fn}, where fn→f, converges to α, the attracting fixed point of f, for all complex numbers z, with one possible exception, z0. I.e.,Fn(z):=fn∘fn−1∘…∘f1(z)→αWhen z0 exists, Fn(z0)→β, the repelling fixed point of f. Applications include the analytic theory of reverse continued fractions.http://dx.doi.org/10.1155/S016117129200108Xlinear fractional transformationscontinued fractionsfixed points. |
| spellingShingle | John Gill Outer compositions of hyperbolic/loxodromic linear fractional transfomations International Journal of Mathematics and Mathematical Sciences linear fractional transformations continued fractions fixed points. |
| title | Outer compositions of hyperbolic/loxodromic linear fractional transfomations |
| title_full | Outer compositions of hyperbolic/loxodromic linear fractional transfomations |
| title_fullStr | Outer compositions of hyperbolic/loxodromic linear fractional transfomations |
| title_full_unstemmed | Outer compositions of hyperbolic/loxodromic linear fractional transfomations |
| title_short | Outer compositions of hyperbolic/loxodromic linear fractional transfomations |
| title_sort | outer compositions of hyperbolic loxodromic linear fractional transfomations |
| topic | linear fractional transformations continued fractions fixed points. |
| url | http://dx.doi.org/10.1155/S016117129200108X |
| work_keys_str_mv | AT johngill outercompositionsofhyperbolicloxodromiclinearfractionaltransfomations |