## Rocky Mountain Journal of Mathematics

### On R.A. Smith's Autonomous Convergence Theorem

#### Article information

Source
Rocky Mountain J. Math., Volume 25, Number 1 (1995), 365-378.

Dates
First available in Project Euclid: 5 June 2007

https://projecteuclid.org/euclid.rmjm/1181072289

Digital Object Identifier
doi:10.1216/rmjm/1181072289

Mathematical Reviews number (MathSciNet)
MR1340014

Zentralblatt MATH identifier
0841.34052

#### Citation

Li, Michael Y.; Muldowney, James S. On R.A. Smith's Autonomous Convergence Theorem. Rocky Mountain J. Math. 25 (1995), no. 1, 365--378. doi:10.1216/rmjm/1181072289. https://projecteuclid.org/euclid.rmjm/1181072289

#### References

• W.A. Coppel, Stability and asymptotic behavior of differential equations, Heath, Boston, 1965.
• V.A. Boichenko and G.A. Leonov, Frequency bounds of Hausdorff dimensionality of attractors of nonlinear systems, Differentsial'nye Uravneniya 26 (1990), 555-563 (Russian). Translated in Ord. Diff. Eqns. 26 (1990), 399-406.
• A. Eden, Local Lyapunov exponents and a local estimate of Hausdorff dimension, Mathematical Modelling and Numerical Analysis 23 (1989), 405-413.
• A. Eden, C. Foias and R. Temam, Local and global Lyapunov exponents, J. Dynamics Differential Equations 3 (1991), 133-177.
• K.J. Falconer, Fractal geometry: Mathematical foundations and applications, Wiley, New York, Chichester, 1990.
• J. Guckenheimer and P.J. Holmes, Nonlinear oscillations, dynamical systems, and bifurcation of vector fields, Springer-Verlag, New York, 1983.
• P. Hartman and C. Olech, On global asymptotic stability of solutions of differential equations, Trans. Amer. Math. Soc. 104 (1962), 154-178.
• U. Kirchgraber and K.J. Palmer, Geometry in the neighborhood of invariant manifolds of maps and flows and linearization, Pitman Research Notes in Mathematics Series #233, Longman Scientific and Technical, Harlow, 1990.
• J.P. LaSalle, The stability of dynamical systems, Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1976.
• Y. Li and J.S. Muldowney, On Bendixson's criterion, J. Differential Equations 106 (1994), 27-39.
• A.W. Marshall and I. Olkin, Inequalities: Theory of majorization and its applications, Academic Press, New York, 1979.
• R.H. Martin, Jr., Logarithmic norms and projections applied to linear differential systems, J. Math. Anal. Appl. 45 (1974), 432-454.
• J.S. Muldowney, Dichotomies and asymptotic behaviour for linear differential systems, Trans. Amer. Math. Soc. 283 (1984), 465-484.
• --------, Compound matrices and ordinary differential equations, Rocky Mountain J. Math. 20 (1990), 857-872.
• C.C. Pugh, The closing lemma, Amer. J. Math. 89 (1967), 956-1009.
• --------, An improved closing lemma and the general density theorem, Amer. J. Math. 89 (1967), 1010-1021.
• C.C. Pugh and C. Robinson, The $C^1$ closing lemma including Hamiltonians, Ergodic Theory Dynamical Systems 3 (1983), 261-313.
• B. Schwarz, Totally positive differential systems, Pacific J. Math. 32 (1970), 203-229.
• R.A. Smith, Some applications of Hausdorff dimension inequalities for ordinary differential equations, Proc. Roy. Soc. Edinburgh Sec. A 104 (1986), 235-259.
• R. Temam, Infinite-dimensional dynamical systems in mechanics and physics, Springer-Verlag, New York, 1988.