Emerging attractors and the transition from dissipative to conservative dynamics

Christian S Rodrigues, Alessandro P S de Moura, Celso Grebogi

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


The topological structure of basin boundaries plays a fundamental role in the sensitivity to the final state in chaotic dynamical systems. Herewith we present a study on the dynamics of dissipative systems close to the Hamiltonian limit, emphasizing the increasing number of periodic attractors, and on the structural changes in their basin boundaries as the dissipation approaches zero. We show numerically that a power law with nontrivial exponent describes the growth of the total number of periodic attractors as the damping is decreased. We also establish that for small scales the dynamics is governed by effective dynamical invariants, whose measure depends not only on the region of the phase space but also on the scale under consideration. Therefore, our results show that the concept of effective invariants is also relevant for dissipative systems.

Original languageEnglish
Article number026205
Number of pages8
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number2
Publication statusPublished - Aug 2009

Bibliographical note

A paid open access option is available for this journal. Link to publisher version required Publisher copyright must be acknowledged Publisher's version/PDF can be used on author's or employers web site (including institutional repository), but not "on e-print servers" or shared repositories Authors version can be used on e-print servers Publisher last contacted on 29/02/2012


  • chaos
  • fractals
  • topology
  • basin boundaries
  • complexity
  • dimension
  • systems
  • cells


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