Geodesic
Escaping subsets of cosine functions with the given Hausdorff dimension
Filomat, Tome 36 (2022) no. 19, p. 6553

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DOI

The escaping set is the important object studied in dynamics of transcendental entire functions. As exponential function is the most typical transcendental entire function, its escaping set has been deeply studied. It is well known that if the function is slightly disturbed, the properties of its dynamical system may vary greatly. We can't easily study different functions in the same way. Contrasting exponential function, we pay our main attention to the cosine function in this paper. We construct some escaping subsets of cosine function by Devaney-Krych codes so that the Hausdorff dimension of the subsets is equal to the given number in the interval (1, 2).
DOI : 10.2298/FIL2219553H
Classification : 30D05, 37F10, 37F35
Keywords: Devaney-Krych code, Hausdorff dimension, escaping point, cosine function 
Xiaojie Huang; Zhixiu Li; Chun Wu. Escaping subsets of cosine functions with the given Hausdorff dimension. Filomat, Tome 36 (2022) no. 19, p. 6553 . doi: 10.2298/FIL2219553H
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     title = {Escaping subsets of cosine functions with the given {Hausdorff} dimension},
     journal = {Filomat},
     pages = {6553 },
     year = {2022},
     volume = {36},
     number = {19},
     doi = {10.2298/FIL2219553H},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2219553H/}
}
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