Invisible parts of attractors ∗

@inproceedings{Ilyashenko2009InvisiblePO,
  title={Invisible parts of attractors ∗},
  author={Yu. Ilyashenko and Andrei Negut},
  year={2009}
}
This paper deals with the attractors of generic dynamical systems. We introduce the notion of ε−invisible set, which is an open set in which almost all orbits spend on average a fraction of time no greater than ε. For extraordinarily small values of ε (say, smaller than 2−100), these are areas of the phase space which an observer virtually never sees when following a generic orbit. We construct an open set in the space of all dynamical systems which have an ε−invisible set that includes parts… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 17 references

Hierarchy of attractors for Axiom A diffeomorphisms

  • A. Gorodetski
  • Vestnik MSU,
  • 1996
Highly Influential
3 Excerpts

Nonremovability of zero Lyapunov exponents

  • A. S. Gorodetskiii, Yu. S. Ilyashenko, V. A. Kleptsyn, M. B. Nalski
  • (Russian) Funktsional Anal. i Prilozhen
  • 2005
1 Excerpt

Nonremovability of zero Lyapunov exponents . ( Russian ) Funktsional Anal

  • A. S. Gorodetskiii, Yu. S. Ilyashenko, V. A. Kleptsyn, M. B. Nalski
  • Proc . Steklov Inst . Math .
  • 2000

Some properties of skew products over a horseshoe and a solenoid

  • A. S. Gorodetskii, Yu. S. Ilyashenko
  • (Russian) Tr. Mat. Inst. Steklova
  • 2000
2 Excerpts

Some new robust properties of invariant sets and attractors of dynamical systems. (Russian) Funktsional

  • A. S. Gorodetskii, Yu. S. Ilyashenko
  • Anal. i Prilozhen
  • 1999
2 Excerpts

Differentiation of SRB states

  • D. Ruelle
  • Commun. Math. Phys
  • 1997
1 Excerpt

Minimal and strange attractors

  • A. S. Gorodetskii, Yu. S. Ilyashenko
  • International Journal of Bifurcation and Chaos,
  • 1996
1 Excerpt

Similar Papers

Loading similar papers…