On a discrete version of the Jacobian conjecture of dynamical systems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 34, Issue 5, 1998, Pages 779-789

  Shih, Mau Hsiang ^a   Wu, Jinn Wen ^a  

^a CHUNG YUAN CHRISTIAN UNIVERSITY   (Taiwan)

Author keywords

Discrete dynamical systems; Global asymptotic stability; Slowly state varying condition; Spectral radius

Indexed keywords

ASYMPTOTIC STABILITY; DIFFERENCE EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; SET THEORY; THEOREM PROVING;

DISCRETE DYNAMICAL SYSTEMS; JACOBIAN CONJECTURE; LASALLE PROBLEMS; SECOND ORDER NONLINEAR DIFFERENCE EQUATIONS; STEIN-TAUSSKY THEOREM;

NUMERICAL METHODS;

EID: 0032353716     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00661-5     Document Type: Article

References (10)

1. W.J. Baumol, Economic Dynamics, 2nd ed., Macmillan, New York, 1959.
2. W. Hahn, Uber die Anwendung der Methode von Lyapunov auf Differenzengleichen, Math. Ann. 136 (1958) 430-441.
3. J. LaSalle, The Stability of Dynamical Systems, Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1976.
4. L. Markus, H. Yamabe, Global stability criteria for differential equations, Osaka Math. J. 12 (1960) 305-317.
5. G.H. Meisters, Jacobian problems in differential equations and algebraic geometry, Rocky Mountain J. Math. 12 (1982) 679-705.
6. J.M. Ortega, W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, London, 1970.
7. R. Redheffer, Remarks on a paper of Taussky, J. Algebra 2 (1965) 42-47.
8. M.-H. Shih, J.-W. Wu, Question of global asymptotic stability in state-varying nonlinear systems, Proc. Amer. Math. Soc. 122 (1994) 801-804.
9. Stein, Some general theorems on iterants, J. Res. Nat. Bur. Standards 48 (1952) 82-83.
10. n→0, J. Algebra 1 (1960) 5-10.