Emerging attractors and the transition from dissipative to conservative dynamics

• Main Authors: Rodrigues, Christian S, de Moura, Alessandro P. S, Grebogi, Celso
• Format: Journal Article
• Language: English
• Published: 17-07-2009
• Subjects: Physics - Chaotic Dynamics
• DOI: 10.48550/arxiv.0808.3954

Physical Review E 80, 026205 (2009) The topological structure of basin boundaries plays a fundamental role in the
sensitivity to the initial conditions in chaotic dynamical systems. Herewith we
present a study on the dynamics of dissipative systems close to the Hamiltonian
limit, emphasising 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
\emph{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.