%0 Journal Article %1 Hegger97 %A Hegger, Rainer %A Kantz, Holger %A Olbrich, Eckehard %D 1997 %J Phys. Rev. E %K dimension intermittency nld ntsa %N 1 %T Correlation Dimension of Intermittent Signals %U http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.3692 %V 56 %X We investigate the breaking of proper self similarity of attractors in the presence of intermittency. We show that this can lead to dramatically too small values of the numerically estimated correlation dimension D 2 , which we relate, in the case of type I intermittency, to universal scaling properties in the vicinity of the critical value of the control parameter. For spatially extended systems we study the influences of space time intermittency on the correlation dimension. The estimation of invariant quantities like dimensions, entropies or Lyapunov exponents has become a quite ubiquitous task in the analysis of chaotic time series. It is impossible to perform numerically the limits given in the mathematical definition of these quantities, since the attractors formed by time series are usually represented by a finite number of points and experimental observables are additionally corrupted by noise. In the case of 'well behaving' low dimensional systems this is not a severe proble...

@article{Hegger97, abstract = {We investigate the breaking of proper self similarity of attractors in the presence of intermittency. We show that this can lead to dramatically too small values of the numerically estimated correlation dimension D 2 , which we relate, in the case of type I intermittency, to universal scaling properties in the vicinity of the critical value of the control parameter. For spatially extended systems we study the influences of space time intermittency on the correlation dimension. The estimation of invariant quantities like dimensions, entropies or Lyapunov exponents has become a quite ubiquitous task in the analysis of chaotic time series. It is impossible to perform numerically the limits given in the mathematical definition of these quantities, since the attractors formed by time series are usually represented by a finite number of points and experimental observables are additionally corrupted by noise. In the case of 'well behaving' low dimensional systems this is not a severe proble...}, added-at = {2014-08-20T19:30:55.000+0200}, author = {Hegger, Rainer and Kantz, Holger and Olbrich, Eckehard}, biburl = {https://www.bibsonomy.org/bibtex/2ae1c8672584f0c630e36ae57cad2c6a6/adisaurabh}, description = {CiteSeerX — Correlation Dimension of Intermittent Signals}, interhash = {dddc27346ed59c5295b8a5dd924aa073}, intrahash = {ae1c8672584f0c630e36ae57cad2c6a6}, journal = {Phys. Rev. E}, keywords = {dimension intermittency nld ntsa}, number = 1, timestamp = {2014-08-20T19:30:55.000+0200}, title = {Correlation Dimension of Intermittent Signals}, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.3692}, volume = 56, year = 1997 }