Dynamics of the radix expansion map
The chaotic dynamics of the map ϕ(x)=(βx+α)(mod1) are studied using Parry's β-expansion. It is shown that for 1<β<2, a≥0, the number of periodic points of period n is 0(βn).
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171294000190 |
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| _version_ | 1832562710036873216 |
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| author | Ben Goertzel Harold Bowman Richard Baker |
| author_facet | Ben Goertzel Harold Bowman Richard Baker |
| author_sort | Ben Goertzel |
| collection | DOAJ |
| description | The chaotic dynamics of the map ϕ(x)=(βx+α)(mod1) are studied using Parry's β-expansion. It is shown that for 1<β<2, a≥0, the number of periodic points of period n is 0(βn). |
| format | Article |
| id | doaj-art-e781f4f4f37a46f1bc9beb865f453c6a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e781f4f4f37a46f1bc9beb865f453c6a2025-02-03T01:22:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117114314610.1155/S0161171294000190Dynamics of the radix expansion mapBen Goertzel0Harold Bowman1Richard Baker2Department of Mathematics, University of Nevada, Las Vegas, Las Vegas 89154, NV, USADepartment of Mathematics, University of Nevada, Las Vegas, Las Vegas 89154, NV, USADepartment of Mathematics, University of Nevada, Las Vegas, Las Vegas 89154, NV, USAThe chaotic dynamics of the map ϕ(x)=(βx+α)(mod1) are studied using Parry's β-expansion. It is shown that for 1<β<2, a≥0, the number of periodic points of period n is 0(βn).http://dx.doi.org/10.1155/S0161171294000190dynamicschaosradix expansion mapinvariant measure. |
| spellingShingle | Ben Goertzel Harold Bowman Richard Baker Dynamics of the radix expansion map International Journal of Mathematics and Mathematical Sciences dynamics chaos radix expansion map invariant measure. |
| title | Dynamics of the radix expansion map |
| title_full | Dynamics of the radix expansion map |
| title_fullStr | Dynamics of the radix expansion map |
| title_full_unstemmed | Dynamics of the radix expansion map |
| title_short | Dynamics of the radix expansion map |
| title_sort | dynamics of the radix expansion map |
| topic | dynamics chaos radix expansion map invariant measure. |
| url | http://dx.doi.org/10.1155/S0161171294000190 |
| work_keys_str_mv | AT bengoertzel dynamicsoftheradixexpansionmap AT haroldbowman dynamicsoftheradixexpansionmap AT richardbaker dynamicsoftheradixexpansionmap |