Mailing address: College of Engineering, Mathematics and Physical Sciences, Harrison Building, University of Exeter, Exeter EX4 4QF, U.K.

2020/2021 Teaching:

2019/2020 Teaching:

Lecture notes:

ELE.

I am one of the organizers of the program TWO-DIMENSIONAL MAPS at the Mittag-Leffler Institute in Stockholm

18 January -- 28 April 2023

Research interests:

Publications:

• Book: One-Dimensional Dynamical Systems: An Example-Led Approach. Chapman and Hall/CRC; 1st edition (11 Aug. 2021). 118 pages.

• A survey on computing the topological entropy of cubic polynomials (with N. Cockram). Indagationes Mathematicae, Volume 32, Issue 4, 2021, Pages 833--846

• Expansion properties of Double Standard Maps (with M. Benedicks and M. Misiurewicz). Preprint version 2020
• Dynamics of planar piecewise isometries: Recent advances (with P. Peres). Published in the special volume for celebrating the 100th anniversary of the Portuguese Mathematical Society Preprint version 2019
• Existence of non-trivial embeddings of interval exchange transformations into Piecewise Isometries (with P. Peres). Preprint version 2019
• On the dynamics of translated cone exchange transformations (with P. Peres). Preprint version 2018
• Fair measures for countable-to-one maps (with S. Roth and Z. Roth). Stochastics and Dynamics. 21 (2021), no. 02, 2150008 Preprint version 2018
• Embeddings of interval exchange transformations into planar piecewise isometries (with P. Ashwin, A. Goetz, P. Peres). Ergod. Th. & Dynam. Sys. Volume 40, 2020, 1153 -- 1179 Preprint version 2018
• Fair measure and fair entropy for non Markov interval maps (with Y. Zhang). Stochastics and Dynamics. 17 (2017), no. 5, 1750035 Preprint version
• Counting preimages (with M. Misiurewicz). Ergod. Th. & Dynam. Sys. Volume 38, Issue 5 (2018) , pp. 1837--1856 Preprint version
• Chaos in generically coupled phase oscillator networks with nonpairwise interactions (with C. Bick and P. Ashwin). Chaos 26 (2016) 094814 Preprint version
• Hopf normal form with SN symmetry and reduction to systems of nonlinearly coupled phase oscillators (with P. Ashwin). Physica D: Nonlinear Phenomena Volume 325, (2016), Pages 14–24 Preprint version
• On the dynamics of a system that bridges the gap between Lorenz and Chen systems. (with J. Llibre). Internat. J. Bifur. Chaos Appl. Sci. Engrg. 25 (2015), no. 9, 1550122
• Periodic orbits for real planar polynomial vector Fields of degree n having n invariant straight lines. (with J. Llibre). Electron. J. Qual. Theory Differ. Equ. (2015) Paper No. 55, 15 pp.
• A non-autonomous kind of Duffing equation (with J. Llibre). Applied Mathematics and Computation , 251 (2015), 669--674.
• Ergodicity of Avalanche Transformations (with M. Denker). Dynamical Systems 29 (2014), 517--536.
• On the limit cycles of the Floquet differential equations (with J. Llibre). Discrete and Continuous Dynamical Systems Ser. B 19 (2014), 1129--1136.
• A note on the periodic orbits of a kind of Duffing equations. (with J. Llibre). Applied Mathematics and Computation , 219 (2013), no. 15, 8358--8365.
• Turning numbers for periodic orbits of disk homeomorphisms (with M. Misiurewicz). Journal of Fixed Point Theory and Applications , 13 (2013), 241--258.
• Fixed points for positive permutation braids (with M. Misiurewicz). Fund. Math. 216 (2012), 129 -- 146
• Non-generic cusps (with M. Misiurewicz). Trans. of the Amer. Mathem. Soc. 363 (2011), 3553--3572.
• On the periodic orbits of Hamiltonian systems (with J. Llibre), J. Math. Phys. 51 (2010), 042704 12pp
• Kneading sequences for double standard maps (with M. Benedicks). Fund. Math. 206 (2009), 61--75.
• Generating Functions for Hopf Bifurcation with $S_n$-Symmetry (with A.P.S.Dias and P.C.Matthews). Disc. and Cont. Dyn. Systems - A 25 (2009), 823--842.
• Hopf bifurcation with $S_n$ symmetry (with A.P.S.Dias). Nonlinearity 22 (2009), 627--666.
• On the tip of the tongue (with M. Misiurewicz). J. of Fixed Point Th. and Applic. 3 (2008), 131--141.
• Double standard maps (with M. Misiurewicz). Commun. in Mathem. Phys. 273 (2007), 37--65.
• Secondary bifurcations in systems with all-to-all coupling. II. (with A.P.S. Dias), Dyn. Syst. 21 (2006), 439--463
• Real 3x+1 (with M. Misiurewicz). Proc. of the Amer. Mathem. Soc. 133 (2005), 1109--1118.