4 papers
Rate of convergence of the -torsion function to the distance function
Farid Bozorgnia, Masoud Bayrami-Aminlouee, Khudoyor Mamayusupov
We prove that the Dirichlet -torsion function converges to the distance to the boundary at the rate in the uniform norm, on every bounded domain and with a co…
Effective Intrinsic Ergodicity for renewal-type potentials on S-gap shifts
Farhod Haydarov, Shirali Kadyrov, Mirmukhsin Makhmudov +1
We establish effective intrinsic ergodicity for renewal-type potentials on one-sided \(S\)-gap shifts. Inducing on the one-symbol cylinder \([1]\) reduces the system to a full shif…
Limit-Cycle Replication via Chebyshev Pullbacks and a Quadratic Ceiling for Separable Schemes
Olimjon Eshkobilov, Shirali Kadyrov, Khudoyor Mamayusupov
Let \(H(n)\) denote the Hilbert number, i.e.\ the maximal number of limit cycles of planar polynomial vector fields of degree \(\le n\). A classical lower-bound mechanism for \(H(n…
Dynamics on immediate basins for parabolic Newton maps
Khudoyor Mamayusupov
Dynamics on parabolic immediate basins for rational Newton maps of entire functions have been studied. It is proved that every parabolic immediate basin contains invariant accesses…