Low Dimensional Dynamics

Focus of research:

Strange attractors are a by now well-known phenomenon in chaotic dynamical systems. Although not the only of its kind, Hénon attractor is a standard and extensively studied component of chaotic dynamics. Despite being the center of intensive research for over three decades, the Hénon and other horseshoe-like strange attractors are still poorly understood.

An inverse limit space with a single bonding map can be seen as the collection of all backward orbits of a dynamical system of the bonding map. Unimodal inverse limits model (to some extend) the Hénon-like attractors, but they are also sufficiently complicated themselves to leave us with many questions.

Key publications:

  1. H. Bruin, S. Štimac, Entropy of homeomorphisms on unimodal inverse limit spaces, Nonlinearity 26 (2013), 991 - 1000.
  2. M. Barge, R. F. Williams, S. Štimac, Pure discrete spectrum in substitution tiling spaces, Discrete and Continuous Dynamical Systems - Series A 33 (2013), 579 - 597.
  3. M. Barge, H. Bruin, S. Štimac, The Ingram Conjecture, Geometry and Topology 16 (2012), 2481 - 2516.
  4. H. Bruin, S. Štimac, On isotopy and unimodal inverse limit spaces, Discrete and Continuous Dynamical Systems - Series A 32 (2012), 1245 - 1253.