Astrofluiddynamics and Astromathematics
Vortices in a Keplerian flow References		A model of a cosmic fractal References
A strange attractor from a model of oscillatory convection References		Nonlinear solitary waves from oscillatory convection at large aspect ratio References
Saddle-loop bifurcation in a third order nonlinear system of ODEs References		Localized oscillations arising in the complex Ginzburg-Landau equation with quintic terms References

Selected Publications

• Keplerian disks

  1. ``Stellar and jovian vortices'', (with T.E. Dowling), in fifth Florida Workshop on Nonlinear Astrophysics, S. Gottesman and J.R. Buchler, eds. Ann. N. Y. Acad. Sci., 617, 190-216 (1990)
  2. ``Spotted Disks'', (with A. Bracco, A. Provenzale and P.A. Yecko) in Theory of Black Hole Accretion Disks, M. Abramowicz, G. Bjornsen & J. Pringle, eds., Cambridge Univ. Press (1998)
  3. ``Particle Aggregation in Keplerian Flows,'' (with A. Bracco, P.-H. Chavanis and A. Provenzale), Phys. Fluids 11 , 2280 (1999)
  
  

• Cosmic fractal

  1. ``Lacunarity and Intermittency in Fluid Turbulence'', (with L.A. Smith and J.-D. Fournier), Phys. Lett. A, 114, 465 (1986)
  2. ``The Dimensions of Cosmic Fractals'', (with R. Thieberger and L.A. Smith) in The Ubiquity of Chaos, S. Krasner, ed., (AAAS Pubs.) Chap. 16 (1990)
  3. ``Cosmic lacunarity'', (with A. Provenzale and R. Thieberger) Chaos, 7, 82-88 (1997)
  4. ``Density singularities and cosmic structures'', (with G. Murante, A. Provenzale and R. Thieberger), Mon. Not. Roy. astr. Soc., 291, 585-592 (1997)
  5. ``Scaling Regimes in the Distribution of Galaxies'', (with G. Murante, A. Provenzale and R. Thieberger) in Nonlinear Dynamics and Chaos in Astrophysics, J.R. Buchler, S.T. Gottesman & H.E. Kandrup, eds., Ann. N. Y. Acad. Sci., 867, 258-267 (1998)
  
  

• A strange attractor

  1. ``A Thermally Excited Nonlinear Oscillator'', (with D. W. Moore), Ap. J., 143, 871 (1966)
  2. ``Aperiodic Behavior of a Non-Linear Oscillator'', (with N. H. Baker and D. W. Moore), Quar. Jour. Mech. and Applied Math., 24, 391 (1971)
  3. ``Ordinary Differential Equations with Strange Attractors'', (with C. J. Marzec), SIAM J. Applied Math., 38, 387 (1980)
  4. ``Chaos in a Finite Macroscopic System'', (with A. Arneodo and P.H. Coullet), Phys. Lett. A, 92, 368 (1982)
  
  

• Solitary waves

  1. ``Intermittency Through Modulational Instability'', (with C.S. Bretherton), Phys. Lett. A, 96, 152 (1983)
  2. ``Chaotic Pulse Trains'', (with N.J. Balmforth and G.R. Ierley), SIAM J. Applied Math. 54 1291-1234 (1994)
  
  

• Saddle-loop

  1. ``Asymptotic Chaos'', (with A. Arneodo, P.H. Coullet and C. Tresser), Physica D 14, 327 (1985)
  2. ``The Dynamics of Triple Convection'', (with A. Arneodo and P.H. Coullet), Geophys. and Astrophys. Fluid Dynamics 31, 1 (1985)
  
  

• Quintic terms

  1. ``The Effect of Radiative Transfer on Convective Growth Rates'', Ap. J., 139, 959 (1964)
  2. ``Asymptotic Chaos'', (with A. Arneodo, P.H. Coullet and C. Tresser), Physica D, 14, 327 (1985)
  
  

• Others

  1. ``Patterns of Aperiodic Pulsation," Astrophys. and Space Sci., 210, 33-49 (1993)
  2. ``The Intermittent Solar Cycle," with N. Platt, and C. Tresser in Geophys. and Astrophys. Fluid Dyn., 73, 146-161 (1993)
  3. ``Topological entropy of one-dimensional maps: approximations and bounds," with N.J. Balmforth and C. Tresser, Phys. Rev. Lett., 72, 80-83 (1994)
  4. ``Advection of Vector Fields by Chaotic Flows," with N.J. Balmforth, P. Cvitanovic, G.R. Ierly, and G. Vatay, in Stochastic Processes in Astrophysics, J.R. Buchler and H. E. Kandrup, eds. Ann. N.Y. Acad. Sci., 706, 148-160 (1994)
  5. ``Autogravity Waves in a Polytropic Layer," with Z.S. Qian Geophys. and Astrophys. Fluid Dyn., 74, 225-244 (1994)
  6. ``Instability in extended systems," with L. Tao, in Proceedings of the Summer Study Program in G.F.D., Woods Hole Oceanographic Institution, R. Salmon, dir., pp. 177-184, WHOI-94-12 (1994)
  7. ``Chaotic Pulse Trains," with N.J. Balmforth and G.R. Ierley SIAM J. Applied Mathematics, 54, 1294-1304 (1994)