Complicated dynamics for low-dimensional strongly monotone maps

Nonlinear Analysis, Theory, Methods and Applications

Volumn 30, Issue 3, 1997, Pages 1911-1914

  Smith, H L ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000602174     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00200-3     Document Type: Article

References (12)

1. COLLET P. & ECKMANN J.-P., Iterated Maps of the Interval as Dynamical Systems, Birkhauser, Boston (1980).
2. DEVANEY R. & NITECKI Z., Shift automorphism in the Henon mapping, Comm. Math. Physics 67, 137-148 (1979).
3. GUCKENHEIMER J. & HOLMES P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, NY (1983).
4. HIRSCH M.W., Stability and convergence in strongly monotone dynamical systems, J. reine angew. Math. 383, 1-53 (1988).
5. MYRBERG P., Iteration der realen polynome zweiten Grades III. Ann. Acad. Scientiarium Fennicae, ser.A 336, 1-18 (1963).
6. POLÁČIK P. & TEREŠČÁK I., Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems, Arch. Rat. Mech. Anal. 116, 339-360 (1991).
7. POLÁČIK P. & TEREŠČÁK I., Exponential separation and invariant bundles for maps in ordered Banach spaces with applications in parabolic equations, J. Dyn.& Diff. Eqn., 279-305 (1993).
8. ROBINSON C., Dynamical Systems, Stability, Symbolic Dynamics, and Chaos, CRC Press, Boca Raton (1995).
9. SMALE S., On the differential equations of species in competition, J. Math. Biol. 3, 5-7 (1976).
10. SMITH H. L., Periodic competitive differential equations and the discrete dynamics of competitive maps, J. Diff. Eqns. 64, 165-194 (1986).
11. SMITH H. L., Periodic solutions of periodic competitive and cooperative systems, SIAM J. Math. Anal. 17, 1289-1318 (1986).
12. 1 smooth strongly monotone discrete-time dynamical systems, preprint (1996).