Finite Approximations of Frobenius-Perron Operators. A Solution of Ulam's Conjecture to Multi-Dimensional Transformations
Physics and Astronomy
Mathematics and Natural Sciences
We prove that Ulam's piecewise constant approximation algorithm is convergent for computing an absolutely continuous invariant measure associated with a piecewise C2 expanding transformation or a Jablonski transformation S: [0, 1]N ⊂ RN → [0, 1]N. This solves an extension of Ulam's conjecture to multi-dimensions and generalizes the convergence result given by T.-Y. Li for one-dimensional transformations.
Physica D: Nonlinear Phenomena
(1996). Finite Approximations of Frobenius-Perron Operators. A Solution of Ulam's Conjecture to Multi-Dimensional Transformations. Physica D: Nonlinear Phenomena, 92(1-2), 61-68.
Available at: https://aquila.usm.edu/fac_pubs/5569