@article{12259,
  abstract     = {Theoretical foundations of chaos have been predominantly laid out for finite-dimensional dynamical systems, such as the three-body problem in classical mechanics and the Lorenz model in dissipative systems. In contrast, many real-world chaotic phenomena, e.g., weather, arise in systems with many (formally infinite) degrees of freedom, which limits direct quantitative analysis of such systems using chaos theory. In the present work, we demonstrate that the hydrodynamic pilot-wave systems offer a bridge between low- and high-dimensional chaotic phenomena by allowing for a systematic study of how the former connects to the latter. Specifically, we present experimental results, which show the formation of low-dimensional chaotic attractors upon destabilization of regular dynamics and a final transition to high-dimensional chaos via the merging of distinct chaotic regions through a crisis bifurcation. Moreover, we show that the post-crisis dynamics of the system can be rationalized as consecutive scatterings from the nonattracting chaotic sets with lifetimes following exponential distributions. },
  author       = {Choueiri, George H and Suri, Balachandra and Merrin, Jack and Serbyn, Maksym and Hof, Björn and Budanur, Nazmi B},
  issn         = {1089-7682},
  journal      = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
  keywords     = {Applied Mathematics, General Physics and Astronomy, Mathematical Physics, Statistical and Nonlinear Physics},
  number       = {9},
  publisher    = {AIP Publishing},
  title        = {{Crises and chaotic scattering in hydrodynamic pilot-wave experiments}},
  doi          = {10.1063/5.0102904},
  volume       = {32},
  year         = {2022},
}

@article{8634,
  abstract     = {In laboratory studies and numerical simulations, we observe clear signatures of unstable time-periodic solutions in a moderately turbulent quasi-two-dimensional flow. We validate the dynamical relevance of such solutions by demonstrating that turbulent flows in both experiment and numerics transiently display time-periodic dynamics when they shadow unstable periodic orbits (UPOs). We show that UPOs we computed are also statistically significant, with turbulent flows spending a sizable fraction of the total time near these solutions. As a result, the average rates of energy input and dissipation for the turbulent flow and frequently visited UPOs differ only by a few percent.},
  author       = {Suri, Balachandra and Kageorge, Logan and Grigoriev, Roman O. and Schatz, Michael F.},
  issn         = {1079-7114},
  journal      = {Physical Review Letters},
  keywords     = {General Physics and Astronomy},
  number       = {6},
  publisher    = {American Physical Society},
  title        = {{Capturing turbulent dynamics and statistics in experiments with unstable periodic orbits}},
  doi          = {10.1103/physrevlett.125.064501},
  volume       = {125},
  year         = {2020},
}

@article{6779,
  abstract     = {Recent studies suggest that unstable recurrent solutions of the Navier-Stokes equation provide new insights
into dynamics of turbulent flows. In this study, we compute an extensive network of dynamical connections
between such solutions in a weakly turbulent quasi-two-dimensional Kolmogorov flow that lies in the inversion symmetric subspace. In particular, we find numerous isolated heteroclinic connections between different
types of solutions—equilibria, periodic, and quasiperiodic orbits—as well as continua of connections forming
higher-dimensional connecting manifolds. We also compute a homoclinic connection of a periodic orbit and
provide strong evidence that the associated homoclinic tangle forms the chaotic repeller that underpins transient
turbulence in the symmetric subspace.},
  author       = {Suri, Balachandra and Pallantla, Ravi Kumar and Schatz, Michael F. and Grigoriev, Roman O.},
  issn         = {2470-0053},
  journal      = {Physical Review E},
  number       = {1},
  publisher    = {American Physical Society},
  title        = {{Heteroclinic and homoclinic connections in a Kolmogorov-like flow}},
  doi          = {10.1103/physreve.100.013112},
  volume       = {100},
  year         = {2019},
}

@article{136,
  abstract     = {Recent studies suggest that unstable, nonchaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role of unstable equilibrium solutions and their invariant manifolds in a weakly turbulent, electromagnetically driven, shallow fluid layer. Identifying instants when turbulent evolution slows down, we compute 31 unstable equilibria of a realistic two-dimensional model of the flow. We establish the dynamical relevance of these unstable equilibria by showing that they are closely visited by the turbulent flow. We also establish the dynamical relevance of unstable manifolds by verifying that they are shadowed by turbulent trajectories departing from the neighborhoods of unstable equilibria over large distances in state space.},
  author       = {Suri, Balachandra and Tithof, Jeffrey and Grigoriev, Roman and Schatz, Michael},
  journal      = {Physical Review E},
  number       = {2},
  publisher    = {American Physical Society},
  title        = {{Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow}},
  doi          = {10.1103/PhysRevE.98.023105},
  volume       = {98},
  year         = {2018},
}