A generalization of Zeeman’s family

• Autorzy: Michał Sierakowski
• Języki publikacji: EN

Abstrakty

EN

E. C. Zeeman [2] described the behaviour of the iterates of the difference equation $x_{n+1} = R(x_n,x_{n-1},...,x_{n-k})/Q(x_n,x_{n-1},..., x_{n-k})$, n ≥ k, R,Q polynomials in the case $k = 1, Q = x_{n-1}$ and $R = x_n+α$, $x_1,x_2$ positive, α nonnegative. We generalize his results as well as those of Beukers and Cushman on the existence of an invariant measure in the case when R,Q are affine and k = 1. We prove that the totally invariant set remains residual when the coefficients vary.

Kategorie tematyczne

• 39A10: Difference equations, additive

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 162
• Numer: 3
• Strony: 277-286

Daty

wydano

1999

otrzymano

1999-01-15

poprawiono

1999-05-20

Twórcy

autor

Michał Sierakowski

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

• [1] F. Beukers and R. Cushman, Zeeman's monotonicity conjecture, J. Differential Equations 143 (1998), 191-200.
• [2] E. C. Zeeman, A geometric unfolding of a difference equation, J. Difference Equations Appl., to appear.
• [3] E. C. Zeeman, Higher dimensional unfoldings of difference equations, lecture notes, ICTP Conference, Trieste, September 1998.