2025/01/10 by Finch, Steven
#26A18 #37E05 #39A20 (Primary) 11B37 #41A60 #65D20 (Secondary) #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2501.06065
The nonlinear recurrences we consider here include the functions 3x(1-x) and cos(x), which possess attractive fixed points 2/3 and 0.739... (Dottie's number). Detailed asymptotics for oscillatory convergence are found, starting with a 1960 paper by Wolfgang Thron. Another function, x/(1+xln(1+x)), gives rise to a sequence with monotonic convergence to 0 but requires substantial work to calculate its associated constant C.