TY - JOUR
T1 - Takens' the last problem and Stein-Ulam Spiral Type Maps
AU - Jamilov, Uygun
AU - Mukhamedov, Farrukh
N1 - Publisher Copyright:
© 2023 Elsevier Inc.
PY - 2024/3/1
Y1 - 2024/3/1
N2 - The main issue of Takens' problem is solved by introducing a new class of stochastic operators called Stein-Ulam Spiral type (SUS-t) maps on a finite-dimensional simplex. Each SUS-t map is established as non-ergodic, i.e., it possesses historical behaviour. Through the usage of the new introduced class, it propels the work forward with focus on the power of the SUS-t map. Hence this paper establishes that any power of SUS-t map also has historical behaviour. The obvious corollary of the main result is that Takens' last problem [33] is resolved within the class of SUS-t maps.
AB - The main issue of Takens' problem is solved by introducing a new class of stochastic operators called Stein-Ulam Spiral type (SUS-t) maps on a finite-dimensional simplex. Each SUS-t map is established as non-ergodic, i.e., it possesses historical behaviour. Through the usage of the new introduced class, it propels the work forward with focus on the power of the SUS-t map. Hence this paper establishes that any power of SUS-t map also has historical behaviour. The obvious corollary of the main result is that Takens' last problem [33] is resolved within the class of SUS-t maps.
KW - Historic behaviour
KW - Non-ergodic operator
KW - Simplex
KW - Stein Ulam spiral map
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U2 - 10.1016/j.jmaa.2023.127813
DO - 10.1016/j.jmaa.2023.127813
M3 - Article
AN - SCOPUS:85173737887
SN - 0022-247X
VL - 531
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
M1 - 127813
ER -