When the long-time behavior is independent of the initial density

SIAM Journal on Mathematical Analysis

Volumn 27, Issue 1, 1996, Pages 221-240

  Lasota, Andrzej ^a,b   Yorke, James A ^c  

^a UNIVERSITY OF SILESIA   (Poland)

^b UNIVERSITY OF MINNESOTA   (United States)

^c UNIVERSITY OF MARYLAND   (United States)

Author keywords

Asymptotic behavior; Expanding mapping; Frobenius Perron operator; Integro differential equation; Invariant density

Indexed keywords

EID: 0030558145     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/0527012     Document Type: Article

References (19)

1. [A] A. AVEZ, Propriétés ergodiques des endomorphismes dilatantes des variétés compactes, C. R. Acad. Sci. Paris Sér A, 266 (1968), pp. 610-612.
2. [B] P. J. BUSHELL, Hilbert's metric and positive contraction mappings in a Banach space, Arch. Rational Mech. Anal., 52 (1973), pp. 330-338.
3. J. E. COHEN, Ergodic theorems in demography, Bull. Amer. Math. Soc., 1 (1979), pp. 275-295.
4. [F-K] T. FUJIMOTO AND U. KRAUSE, Asymptotic properties for inhomogeneous iterations of nonlinear operators, SIAM J. Math. Anal., 19 (1988), pp. 841-853.
5. [G-K-R] M. GOLUBITSKY, E. KEELER, AND M. ROTHSCHILD, Convergence of the age structure: Applications of the projective metric, Theoret. Population Biol., 7 (1975), pp. 84-93.
6. [K] K. KRZYŻEWSKI, Some results on expanding mappings, Astérisque, 50 (1977), pp. 205-218.
7. [K-S] K. KRZYŻEWSKI AND W. SZLENK, On invariant measures for expanding differential mappings, Studia Math., 33 (1969), pp. 83-92.
8. [L-R] A. LASOTA AND R. RUDNICKI, Asymptotic behaviour of semigroups of positive operators on C(X), Bull. Polish Acad. Sci. Math., 36 (1988), pp. 151-159.
9. [L-Y] A. LASOTA AND J. A. YORKE, Exact dynamical systems and the Frobenius-Perron operator, Trans. Amer. Math. Soc., 273 (1982), pp. 375-384.
10. M. LIN, Mixing for Markov operators, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 19 (1971), pp. 231-242.
11. [Lo] S. LOJASIEWICZ, An Introduction to the Theory of Real Functions, Wiley, New York, 1988.
12. [N] R. D. NUSSBAUM, Some nonlinear weak ergodic theorems, SIAM J. Math. Anal., 21 (1990), pp. 436-460.
13. [P-Y] G. PIANIGIANI AND J. A. YORKE, Expanding maps on sets which are almost invariants: Decay and chaos, Trans. Amer. Math. Soc., 252 (1979), pp. 351-366.
14. [Re] A. RÉNYI, Representation for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar., 8 (1957), pp. 477-493.
15. [Rl] D. RUELLE, Statistical mechanics of a one-dimensional lattice gas, manuscript.
16. [Ro] V. A. ROCHLIN, Exact endomorphisms of Lebesgue spaces, Amer. Math. Soc. Transl. Ser. 2, 39 (1964), pp. 1-36.
17. [Ru] R. RUDNICKI, Asymptotic properties of the iterates of positive operators on C(X), Bull. Polish. Acad. Math. Sci., 34 (1986), pp. 181-187.
18. [Se] E. SENETA, Nonnegative Matrices and Markov Chains, Springer-Verlag, New York, 1981.
19. [So] J. SOCALA, On the existence of invariant measures for Markov operators, Ann. Polon. Math., 48 (1988), pp. 51-56.