Research

Research interests

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

Publications

1. Papers

1.      [2009] J. Buescu, D. Graça, M. Campagnolo, Computational bounds on polynomial differential equations. Appl. Math. Comp. 215 (2009), 1375—1385.

2.      [2009] J. Buescu, P. Teixeira, Foam as a geometer. Europh. News, 40 (2009), 3, 21—25.

3.      [2009] J. Buescu, D. Graça, N. Zhong, Computability, noncomputability and undecidability of maximal intervals of IVPs. Trans. Amer. Math. Soc. 361 (2009), no. 6, 29132927.

4.      [2008] J. Buescu, Liapunov stability and the ring of P-adic integers. São Paulo J. Math. Sci. 2 (2008), no. 1, 7784.

5.      [2008] J. Buescu, D. Graça, Boundedness of the domain of definition is undecidable for polynomial odes. Electronic Notes in Theoretical Computer Science, 202: 49-57.

6.      [2008] J. Buescu, D. Graça, M. Campagnolo, Computability with polynomial differential equations. Adv. in Appl. Math. 40 (2008), no. 3, 330349.

7.      [2007] J. Buescu, A. C. Paixão, Eigenvalue distribution of Mercer-like kernels. Math. Nachr. 280 (2007), no. 9-10, 984995.

8.      [2007] J. Buescu, A. C. Paixão, Eigenvalue distribution of positive definite kernels on unbounded domains. Integral Equations Operator Theory 57 (2007), no. 1, 1941.

9.      [2006] J. Buescu, A. C. Paixão, Inequalities for differentiable reproducing kernels and an application to positive integral operators. J. Inequal. Appl. 2006, Art. ID 53743, 9 pp.

10.  [2006] J. Buescu, M. Kulczycki, I. Stewart, Liapunov stability and adding machines revisited. Dyn. Syst. 21 (2006), no. 3, 379384.

11.  [2006] J. Buescu, A. C. Paixão, Eigenvalues of positive integral operators in unbounded intervals. Positivity 10 (2006), no. 4, 627646.

12.  [2006] J. Buescu, A. C. Paixão, Positive definite matrices and reproducing kernel inequalities. J. Math. Anal. Appl., J. Math. Anal. Appl. 320 (2006), no. 1, 279292.

13.  [2006] J. Buescu, A. C. Paixão, Positive definite matrices and integral equations on unbounded domains. Differential and Integral Equations 19, 2 (2006), 189-210.

14.  [2006] J. Buescu, A. C. Paixão, A linear algebraic approach to holomorphic reproducing kernels in Cn . Linear Algebra and its Applications 412 (2006), 270-290.

15.  [2005] 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.

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

17.  [2004] J. Buescu, Positive integral operators in unbounded domains. J. Math. Anal. Appl. 296 (2004), 244--255.

18.  [2001] J. Buescu, F. Garcia, I. Lourtie, L2(R) nonstationary processes and the sampling theorem. IEEE Signal Processing Letters, vol 8, 4 (2001), 117-119.

19.  [1996] J. Buescu, P. Ashwin, I. Stewart, From attractor to chaotic saddle: a tale of transverse instability. Nonlinearity 14 (1996), 355-386.

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

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

2. Conference Proceedings

 

1.  [2009] A. C. Paixão, Algebraic, differential, integral and spectral properties of Mercer-like kernels. More progress in Analysis: Proceedings of the 5th International ISAAC 2005 Conference, 175—188. World Scientific.

2.  [2007] J. Buescu, D. Graça, M. Campagnolo, Boundedness of the domain of definition is undecidable for polynomial ODEs.  Proceedings of the 4th International Conference of Computability and Complexity in Analysis (CCA 2007), Eds. R. Dillhage, T. Grubba, A. Sorbi, K. Weihrauch and N. Zhong.   FernUniversität in Hagen, 127--135

3.  [2006] J. Buescu, D. Graça, N. Zhong, The ordinary differential equation defined by a computable function whose maximal interval of existence is non-computable. In G. Hanrot and P. Zimmermann, editors, Proceedings of the 7th Conference on Real Numbers and Computers (RNC 7), pages 33-40. LORIA/INRIA, 2006.

4.      [2003] J. Buescu, S. Castro, A. Dias, I. Labouriau, Foreword by the editors. Bifurcations, Symmetry and Patterns Conference Proceedings (vii-x),  Birkhäuser, Basel, 2003.

5.      [2002] J. Buescu, F. Garcia, I. Lourtie, Local stationarity of L2(R) processes. IEEE ICASSP Conference Proceedings, vol. II (2002), 1221-1224.

6.      [1998] J. Buescu, Instability of attractors in invariant submanifolds. Equadiff 95 Conference Proceedings, World Scientific, 288-293.

7.       [1994] J. Buescu, I. Stewart, Sets, lines and adding machines. In Dynamics, new trends and new tools, ed. Pascal Chossat, Kluwer, 1994, 59-67.

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. Under co-supervision with M. Campagnolo (ISA). Thesis held on September 2007.
 
M.Sc. students

    1. Helena Aidos: Adding machines e inteiros p-ádicos. Thesis held in December 2007.


Last update: May 11,  2010.