José Ayala



Contact Information


Facultad de Ingeniería y Arquitectura
Universidad Arturo Prat
Iquique, Chile



Research Interests



Differential and computational geometry, low dimensional topology and dynamics.



Education



University of Melbourne, Parkvile, VIC Australia.
Ph.D. in Mathematics, March 2014.
Advisor: Hyam Rubinstein.
Dissertation Topic: Classification of the homotopy classes and minimal length elements in spaces of bounded curvature paths.

Iowa State University, Ames, Iowa USA.
M.Sc. in Mathematics, July 2007.
Advisor: Wolfgang Kliemann.
Thesis Topic: Global behavior of graph dynamics with applications to Markov chains.

Universidad Católica del Norte, Antofagasta, Chile.
B.S. in Mathematics, March 2005.
Advisor: Wolfgang Kliemann.
Thesis Topic: Dynamical systems in the real projective space.



Publications and Preprints



1. J. Ayala. Length minimising bounded curvature paths in homotopy classes. Topology and its Applications, Vol. 193, pp. 140-151, 2015, arXiv:1403.4930.

2. J. Ayala. On the topology of the spaces of curvature constrained plane curves. Accepted in Advances in Geometry, arXiv:1404.4378.

3. J. Ayala and J.H. Rubinstein. The classification of homotopy classes of bounded curvature paths. Accepted in Israel Journal of Mathematics, arXiv:1403.5314.

4. J. Ayala. Connectedness and minimal length elements in spaces of bounded curvature paths. Bulletin of the Australian Mathematical Society, Vol. 90, No 1, pp. 174-176, 2014.

5. J. Ayala and J.H. Rubinstein. Non-uniqueness of the homotopy class of bounded curvature paths. Submitted to Mathematische Zeitschrift, arXiv:1403.4911.

6. J. Ayala, D. Kirszenblat, and J.H. Rubinstein. A geometric approach to shortest bounded curvature paths. Submitted to Communications in Analysis and Geometry, arXiv:1403.4911.

7. J. Ayala and W. Kliemann. Topological dynamics of flows and semiflows associated with graphs. Submitted to Discrete and Continuous Dynamical Systems, arXiv:1501.07509.



Peer-Reviewed Conference Articles



1. J. Ayala-Hoffmann, M. Brazil, H. Rubinstein, D. Thomas, Extendibility and path components of admissible paths for the Dubins problem. Proceedings of Australian Control Conference, 440-444, IEEE - Institute of Electrical and Electronic Engineers, 2011.

2. J. Ayala-Hoffmann, W. Kliemann, Morse decompositions of semiflows associated with graphs. Proceedings of the 20th International Symposium on Mathematical Systems and Networks (MTNS 2012, July 9-13 2012) Melbourne, Australia.

3. J. Ayala-Hoffmann, M. Brazil, H. Rubinstein, D. Thomas, A geometric approach to shortest bounded curvature paths in surfaces of constant non-positive curvature. Proceedings of the 20th International Symposium on Mathematical Systems and Networks (MTNS 2012, July 9-13 2012) Melbourne, Australia.



Undergraduate Research



1. J. Ayala-Hoffmann, P. Corbin, K. Mc Conville, F.Colonius, W. Kliemann. Morse decompositions, attractors and chain recurrence, Proyecciones Journal of Mathematics Vol. 25, No 1, pp. 79-109, 2006.

2. V. Ayala, J. Ayala-Hoffmann, Ivan Tribuzy. Controlability of invariant control systems at uniform time, Kybernetika, Vol. 45, No 3, pp. 405-416, 2009.



Languages



Spanish, Portuguese, Italian and English.



References



Professor Hyam Rubinstein
Department of Mathematics and Statistics,
University of Melbourne,
Parkvile, VIC, Australia.

A/Professor Craig Hodgson
Department of Mathematics and Statistics,
University of Melbourne,
Parkvile, VIC, Australia.

Professor Joel Hass
Department of Mathematics,
University of California,
Davis, CA, USA.



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