GEOPllYSICAL RESEARCt{ I.ETTERS, VOI•. t7, NO• 11,PAGES 184!.1844, OLTFOBER t• LOW-DIMENSIONAL CHAOS IN MAGNETOSPHERIC ACTIV• FROM AE TIME SERIES D. V. Vassi!iadis, A. S. Sharma, T. E. Eastman and K. Papado•ulos University of Maryland, College P.ark, Maryland Abstract. The magnetosphe.ric response m thesolar wind •.•.• , as represented by • time series measurements of the AE'm•x, has been examined using phase space reconstruc- .•d-:•n •hnktues. The system was foundto behave as a low- •{-•m•. nsional chaotic system with a fractal dimension of 3.6 ß .red has a Kolmogorov entropy <0.2/min. Tt•se arei•cafive .•att•e dynamics of thesysmm can be adequate!y described •by f.mir independent variables and a correspon•ng intrinsic 6..n• sc•e is of the order of 5 min. The relevance of the re.•ltsm magnetospheric _modelling is discusse& Introduction • earth's magnetosphere is a complex, non!i-• dy- •.•ical system wMch responds in a relatively tinpredictable f•him to variations of the solar wind energy input. There is e•dence [Gonzalez et al., !989] that tt• southwa• com- •e.nt of the interplanetary magnetic field (IMF) is a key pa•-•:mrr•r thatcontrols the solar wind input. Many indices, e.,g, AE, A U, AL, D•t,Kp, etc. are used to ch.aracterize .•'•;the .magnetospheric response .to thissolar wind input. Each .me_..menures a different type of resprmse [Mayand, 19.80; Baam'•n, 19'861. The auroral electrojet (AE) indexis a •.:ma.sm of the horizontal current strength flowing in the :• ionosphere. It is often takenas the substorm index. ,.Many emph-ical andphysical models attempt to study the mspcm.m of AE to the IMF variations [Clatter et al., I983; '. -.•tze et •., 1985; Kamide and Slavin, i986] us'rag lin- ear prediction filtertechniques. Most r•<enfiy, Tsm,atani et al. [I99•] examinedt• F•er transfore of the AE time •s and correlated it m theIMF spectrum. Themsu!ts of ::•e studies indiesre: i), the absence of pefi• orquasiperi- ,-•. '.•:havior. Rather, thepower is always ccmcentrated in 'f.•t, oa•est •uency suggesting an apedc•c behavior (ei .ther •½•.•erministic•haofic or random); ii) a lff power s.•x:tru.m, '." far mO•e IMF spectrum, atlo..w _•uencies (f<6.10-•Hz) m• a .bve• near 6.!0 -• Hz followed bya 1/fz=-z4spec- •.•.• •m. Namely, -the magnetosphere is a Icrsv-pass filter and m in• d .•amics cones tt• high f•requency behavior. :•'•,F• :•tt• m}•ysics point of view the "inte .real d .ynami½s" }s..cam..posed of a complex of interactions which inv•ve phe- ': :.:• such as mc•ficafionsin the i ..onosp .hen'c conductiv- •, crr•-•l era'rant •m•fion or t •g ,.mlxle Nsmb•ifies, .fi.•::•ali ...gned currents, ..anomalous rresisfivi• or•ble layers, •. AI/15•h prog•ss inu '.•rsmnding "t•se n•r•m,,ena has • made, we m still far from .produ•in;'g quantitative .pre- ':•;•ti.• m•.•ls of the ;mr [Buffer and .:' .Papa. d•ulos, 1990b7 the Amsrican •ophysica! Union, 1984]. The techniqms described above reve•ed the presence of multiple time scales but could not assess the dynamos re- sponsible for theobse•edoutput. It is the ••e of this letter topropose a different type of analysis a• modell• g of the data that describe themagnetospheric response b ..ased on recent developments in thestudy of phase ,spaces of lnoa_inear systems [Mayer-Kress, 19861. Until recently nonlinear systems with :-••c be•hav- ior, such as themagne,•l•ere, were •• im • of power spectra orcorrehtion functions. However, w.hi• tral studies are s•table for t• study, .and classifim.tion of perk•ic, quasiperiodic or-random systems, they are unable to provide ..meaningful information for a wkle class of sys- tems known today as "c'_ .haofic" systems. in s•h systems vhe broadhaM s.pectra and ' •mrkan" behavior apparent 'm snap- shots or time series, -are theconvinces of a_peri•c ministic motion withextreme sensitivity to i•tial • 'nons rather than stoch.asfic behavior. In the past few• niques have been developed which •ow us • &rivequanti- ties assr•ia.ted withthephase-.,space evolution of the and its associated geomet•. • quantifies are -knomas dimensions, emropies, Lya!xm ,nov exponen• •and singul•.•ty spectra [Farmer et al., !983; Mayer-Kress, 1986]. A ,;varec of these quant•es is that t!•y provide s;nnple, g!oba1 _•a• 1o•cally invariant informatioa. The 'dm•n•, forexamp•, withwh;mh we deal mainly in this •per, is a sing•-•rr• .bet information on *• system. It represents • minkm-.• of i•pendem variables 'that candescribe the syaem. Ft•- tt'mmore, from the point of view of ana!y -•g ex•_ •'•aml dam, these quantifies have• v'mne that•y m be culat-• easily frmn 'time series even from a single variable. In thisl•per we presem an •ysis of fin• desof theAE index using nonFme• ':•cal tecb•ues. The •ysis demonsms .that magnetos•c behavior as repre:'sented by the AE index ia a 1ow••siorM ...•attract• •and •us amenable to fu•,r dyn:,,amical ,analysis, ',h v•w of thenovelty of such tec•iq•s in thes!mce physics com- munity we present in the next seerios a mmewMt exmnded description of t• time-,,.•s analysis tecl,m'•. Nonlinear Ti•-Series Av,•ysis A •ssipafive sysmm, such as t• the ,property that its phase space vol; system ap •.•:hes its asymptotic sta•. is called• attractor •and,,may •ge_••y !f we conskt• • a,mact :c• as a 'set • ,t'• phase space..•n by a -wel!•fi .• assign m it a num• called i• di:•nsion. tums outm be a I..'o• ..•.nd in the n•• !841