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Chain recurrence and attractors in general dynamical systems

박종서|이경복
대한수학회 (The Korean Mathematical Society)|2007.10|대한수학회논문집 (Communications of the KMS)|제22권 제4호|pp. 576-586

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주제분류수학

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Abstract

We introduce here notions of chain recurrent sets, attractorsand its basins for general dynamical systems and prove important prop-erties including (i) the chain recurrent setCR(f) off on a metric space(X;d) is the complement of the union of setsB(A) A as A varies over thecollection of attractors and (ii) genericity of general dynamical systems.

참고문헌 (12)

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  2. "Topological theory of dynamical systems" (1994), North-Holland
  3. "Stability theory of dynamical systems" (1970), Springer Verlag
  4. "Asmptotic stablity in general dynamical systems, Non lineerAnalysis Theory", 13, pp.657~669 (1998)
  5. "Chain recurrence and attraction in noncompacr spaces" (1991)
  6. "Lyapunov functions and attractors in arbitrary metric spaces", 126, pp.245~256 (1998)
  7. "Weak attractors from Lyapunov functions", 109, pp.201~210 (2001)
  8. "Topology 2", pp.~2 (1968), Academic Press-PWN-Polish Sci. Pub. Warszawa
  9. "On dynamical stability in general dynamical systems", 263, pp.455~478 (2001)
  10. "The space of dynamical systems with the C0-topology", lecture(tes inmathematics) (1994), Springer-Verlag
  11. "Stability in general control systems" (1965)
  12. "Introduction to topological dynamics", (ordho international pub) (1975)

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