A matrix solution to the inverse Perron-Frobenius problem

Authors:
P. Góra and A. Boyarsky

Journal:
Proc. Amer. Math. Soc. **118** (1993), 409-414

MSC:
Primary 58F11; Secondary 28D05

MathSciNet review:
1129877

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a probability density function on the unit interval . The inverse Perron-Frobenius problem involves determining a transformation such that the one-dimensional dynamical system has as its unique invariant density function. A matrix method is developed that provides a simple relationship between and , where is any piecewise constant density function. The result is useful for modelling and predicting chaotic data.

**[1]**Nathan Friedman and Abraham Boyarsky,*Construction of ergodic transformations*, Adv. in Math.**45**(1982), no. 3, 213–254. MR**673802**, 10.1016/S0001-8708(82)80004-2**[2]**S. V. Ershov and G. G. Malinetskiĭ,*Solution of an inverse problem for the Perron-Frobenius equation*, Zh. Vychisl. Mat. i Mat. Fiz.**28**(1988), no. 10, 1491–1497, 1598 (Russian); English transl., U.S.S.R. Comput. Math. and Math. Phys.**28**(1988), no. 5, 136–141 (1990). MR**973203****[3]**Abraham Boyarsky and Gabriel Haddad,*All invariant densities of piecewise linear Markov maps are piecewise constant*, Adv. in Appl. Math.**2**(1981), no. 3, 284–289. MR**626863**, 10.1016/0196-8858(81)90008-7**[4]**Martin Casdagli,*Nonlinear prediction of chaotic time series*, Phys. D**35**(1989), no. 3, 335–356. MR**1004201**, 10.1016/0167-2789(89)90074-2**[5]**S. Pelikan,*Invariant densities for random maps of the interval*, Trans. Amer. Math. Soc.**281**(1984), no. 2, 813–825. MR**722776**, 10.1090/S0002-9947-1984-0722776-1

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
58F11,
28D05

Retrieve articles in all journals with MSC: 58F11, 28D05

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1993-1129877-8

Article copyright:
© Copyright 1993
American Mathematical Society