Abstract
In this chapter the generalized spectral decomposition of a variety one-dimensional maps is presented. An algebraic technique is introduced and applied to determine the spectral decomposition of the tent map. Some maps with non-diagonalizable decompositions are presented, including a map whose resolvent has an essential singularity. A map that does not preserve Lebesgue measure and where the dynamics settles onto a strange attractor is analyzed. Finally, the decompositions of maps related by a simple change of variables are discussed and the decomposition of the logistic map with unit height is determined from the decomposition of the tent map.
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Bibliographical Notes
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© 1999 Springer Science+Business Media Dordrecht
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Driebe, D.J. (1999). Other One-Dimensional Maps. In: Fully Chaotic Maps and Broken Time Symmetry. Nonlinear Phenomena and Complex Systems, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1628-4_4
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DOI: https://doi.org/10.1007/978-94-017-1628-4_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5168-4
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