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We study the stability properties and long-term dynamical behavior of chimerastates in globally coupled map lattices. In particular, we give a formula forthe transverse Lyapunov exponent associated with blocks of synchronized sites.We use these results to study clustered dynamics from a numerical perspective,and give numerical evidence of attracting chimeras having chaotic dynamics, aswell as periodic behaviors. Finally, we obtain some results ruling out theexistence of absolutely continuous invariant measures supported on chimerastates in strong coupling regimes.

Dynamical properties of chimera states for globally coupled map lattices