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Modern Dynamical Systems Theory

  • L. Markus (a1) (a2)

Abstract

In order to analyse generic or typical properties of dynamical systems we consider the space of all C 1-vector fields on a fixed differentiable manifold M. In the C 1-metric, assuming M is compact, is a complete metric space and a generic subset is an open dense subset or an intersection of a countable collection of such open dense subsets of . Some generic properties (i.e. specifying generic subsets) in are described. For instance, generic dynamic systems have isolated critical points and periodic orbits each of which is hyperbolic. If M is a symplectic manifold we can introduce the space of all Hamiltonian systems and study corresponding generic properties.

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References

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Markus, L.: 1971, Lectures in Differentiable Dynamics , Regional Conference Series in Mathematics No. 3.
Markus, L. and Meyer, K.: 1974, Mem. Am. Math. Soc. (in press).
Robinson, R. C.: 1971, Lectures on Hamiltonian Systems , Instituto de Matematica Pura e Aplicado, Rio de Janeiro, Brazil.
Siegel, C. L. and Moser, J.: 1971, Lectures on Celestial Mechanics , Springer Verlag, New York.
Smale, S.: 1967, Bull. Am. Math. Soc. 73, 747.

Modern Dynamical Systems Theory

  • L. Markus (a1) (a2)

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