%0 Journal Article %1 aubry1991spatiotemporal %A Aubry, Nadine %A Guyonnet, Régis %A Lima, Ricardo %D 1991 %J Journal of Statistical Physics %K 37d45-strange-attractors 37j60-nonholonomic-dynamical-systems 37n99-applications-of-dynamical-systems 62m10-time-series-auto-correlation-regression 76f20-dynamical-systems-approach-to-turbulence 94a12-signal-theory %P 683–739 %R 10.1007/BF01048312 %T Spatiotemporal analysis of complex signals: Theory and applications %U https://link.springer.com/article/10.1007%2FBF01048312 %V 64 %X We present a space-time description of regular and complex phenomena which consists of a decomposition of a spatiotemporal signal into orthogonal temporal modes that we call chronos and orthogonal spatial modes that we call topos. This permits the introduction of several characteristics of the signal, three characteristic energies and entropies (one temporal, one spatial, and one global), and a characteristic dimension. Although the technique is general, we concentrate on its applications to hydrodynamic problems, specifically the transition to turbulence. We consider two cases of application: a coupled map lattice as a dynamical system model for spatiotemporal complexity and the open flow instability on a rotating disk. In the latter, we show a direct relation between the global entropy and the different instabilities that the flow undergoes as Reynolds number increases.

@article{aubry1991spatiotemporal, abstract = {We present a space-time description of regular and complex phenomena which consists of a decomposition of a spatiotemporal signal into orthogonal temporal modes that we call chronos and orthogonal spatial modes that we call topos. This permits the introduction of several characteristics of the signal, three characteristic energies and entropies (one temporal, one spatial, and one global), and a characteristic dimension. Although the technique is general, we concentrate on its applications to hydrodynamic problems, specifically the transition to turbulence. We consider two cases of application: a coupled map lattice as a dynamical system model for spatiotemporal complexity and the open flow instability on a rotating disk. In the latter, we show a direct relation between the global entropy and the different instabilities that the flow undergoes as Reynolds number increases.}, added-at = {2021-07-19T02:09:29.000+0200}, author = {Aubry, Nadine and Guyonnet, Régis and Lima, Ricardo}, biburl = {https://www.bibsonomy.org/bibtex/28b5057947d9880ad0e19b6eeb1018248/gdmcbain}, doi = {10.1007/BF01048312}, interhash = {4ee7039cd4b8b1a9d441855d276ed2f2}, intrahash = {8b5057947d9880ad0e19b6eeb1018248}, journal = {Journal of Statistical Physics}, keywords = {37d45-strange-attractors 37j60-nonholonomic-dynamical-systems 37n99-applications-of-dynamical-systems 62m10-time-series-auto-correlation-regression 76f20-dynamical-systems-approach-to-turbulence 94a12-signal-theory}, pages = {683–739}, timestamp = {2021-07-19T02:11:59.000+0200}, title = {Spatiotemporal analysis of complex signals: Theory and applications}, url = {https://link.springer.com/article/10.1007%2FBF01048312}, volume = 64, year = 1991 }