Research

Research interests
Differential equations, discrete dynamical systems, integral operators, positive-definiteness, reproducing kernels, computability and ODEs.

Publications (published and accepted)

  1. J. Buescu, A. C. Paixão, Eigenvalue distribution of positive definite kernels on unbounded domains. Integr. equ. oper. theory, to appear.

  2. J. Buescu, D. Graça, N. Zhong,  Maximal intervals of computable  IVPs are not necessarily  computable. Trans. Amer. Math. Soc., to appear.
  3. J. Buescu, D. Graça, N. Zhong, An ordinary differential equation defined by a computable function whose maximal interval of existence is non-computable.                                               Proceedings of RNC7, to appear.
  4. J. Buescu, A. C. Paixão, Eigenvalue distribution of Mercer-like kernels. Math. Nachr., to appear.
  5. J. Buescu, A. C. Paixão, Eigenvalues of positive definite integral operators in unbounded intervals. Positivity, to appear.
  6. J. Buescu, A. C. Paixão, Positive definite matrices and differentiable reproducing kernel inequalities. J. Math. Anal. Appl. 320 (2006), 279-292.
  7. J. Buescu, A. C. Paixão, Inequalities for differentiable reproducing kernels and an application to positive integral operators. Journal of Inequalities and Applications, to appear.
  8. J. Buescu, M. Kulczycki, I. Stewart, Liapunov stability and adding machines revisited. Dynamical Systems: an international journal. To appear.
  9. J. Buescu, A. C. Paixão, Algebraic, differential, integral and spectral properties of Mercer-like kernels. ISAAC 2005 Conference Proceedings, World Scientific, to appear. 

  10. J. Buescu, A. C. Paixão, Positive definite matrices and integral equations on unbounded domains. Differential and Integral Equations 19, 2 (2006), 189-210.

  11. J. Buescu, A. C. Paixão, A linear algebraic approach to holomorphic reproducing kernels in Cn . Linear Algebra and its Applications 412 (2006), 270-290. 

  12. J. Buescu, D. Graça, M. Campagnolo, Robust Simulations of Turing Machines with Analytic Maps and Flows. Lecture Notes in Computer Science, 

    Volume 3526, Jan 2005, 169 – 179. 

  13. J. Buescu, F. Garcia, I. Lourtie, A. Paixão, Positive definiteness, integral operators and Fourier transforms. Jour. Int. Eq. Appl. 16, 1 (2004), 33--52. 

  14. J. Buescu, Positive integral operators in unbounded domains. J. Math. Anal. Appl. 296 (2004), 244--255. 

  15. J. Buescu, F. Garcia, I. Lourtie, Local stationarity of L2(R) processes. IEEE ICASSP Conference Proceedings, vol. II (2002), 1221-1224. 

  16. J. Buescu, F. Garcia, I. Lourtie, L2(R) nonstationary processes and the sampling theorem. IEEE Signal Processing Letters, vol 8, 4 (2001), 117-119. 

  17. J. Buescu, Instability of attractors in invariant submanifolds. Equadiff 95 Conference Proceedings, World Scientific, 288-293. 

  18. J. Buescu, P. Ashwin, I. Stewart, From attractor to chaotic saddle: a tale of transverse instability. Nonlinearity 14 (1996), 355-386. 

  19. J. Buescu, I. Stewart, Liapunov stability and adding machines. Ergodic Theory and Dynamical Systems 15 (1995), 1-20. 

  20. J. Buescu, I. Stewart, Sets, lines and adding machines. In Dynamics, new trends and new tools, ed. Pascal Chossat, Kluwer, 1994, 59-67. 

  21. J. Buescu, P. Ashwin, I. Stewart, Bubbling of attractors and synchronization of chaotic oscillators. Physics Letters A 193 (1994), 126-139.



Preprints

  1. J. Buescu, A. C. Paixão, Inequalities for holomorphic reproducing kernels. Submitted for publication.
  2. J. Buescu, D. Graça, M. Campagnolo, Computability with polynomial differential equations.  Submitted for publication.

Books

  1. J. Buescu, S. Castro, A. Dias, I. Labouriau (eds.), Bifurcations, symmetry and patterns. Conference Proceedings. Birkhäuser, Basel, 2003.

  2. J. Buescu, Exotic Attractors: from Liapunov stability to riddled basins. Progress in Mathematics 153, Birkhäuser Verlag, Basel, 1997.


Ph.D. students
  1. António Paixão (ISEL):  On algebraic, differential, integral and spectral properties of  Mercer-like kernels.  Thesis held on January 2006.     
  2.  Daniel Graça  (Universidade do Algarve). Subject: Computability and differential equations. Currently under co-supervision with M. Campagnolo (ISA). 
        Thesis expected in 2007.  


Last update: May 31,  2006.