## Ana Rodrigues

Senior Lecturer

Office: 242
Tel: 01392 723988
email:a.rodrigues[at]exeter.ac.uk

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

#### 2018/2019 Teaching:

Analysis

ECM3740 Topology and Metric Spaces (Module Leader)

#### 2017/2018 Teaching:

ECMM702 Methods for Stochastics and Finance (Module Leader)

ECM3740 Topology and Metric Spaces (Module Leader)

Analysis (Tutorials)

Lecture notes:

#### Financial Mathematics/ MMath Students:

Max Gailor. 2017/2018.

Ali Algamedi. 2017/2018.

Huda Alshammari. 2016/2017. Title: Dynamics of Piecewise isometries.

Ana-Maria Pirvu. 2016/2017. Title: The Term Structure of Constant Maturity Swap Yields.

Robert Ashton. 2015/2016. Title: $\alpha$-standard maps.

Chloe Batten. 2014/ 2015. Title: Distributions of Annuities with Stochastic Interest Rates.

#### Phd Students:

• Davit Karagoulyan (KTH -- Royal Institute of Technology, Sweden). Joint with M. Benedicks.

Title: Certain results on the Möbius disjointness conjecture. Finishing in November 2017.

Papers by Davit:

On Möbius orthogonality for interval maps of zero entropy and orientation-preserving circle homeomorphisms Ark. Mat., (2015) 317–327.

On Möbius orthogonality for subshifts of finite type with positive topological entropy Studia Math., (2017) 277–282).

Hausdorff dimension of a class of three-interval exchange maps Preprint: https://arxiv.org/abs/1701.01984

On certain aspects of the Möbius randomness principle Preprint

• Pedro Peres (University of Exeter, UK)
• Papers by Pedro:

Embeddings of interval exchange transformations into planar piecewise isometries. Preprint.

Mary Thoubaan (with Peter Ashwin)

Ummu Atiqah Mohd Roslan (with Peter Ahswin)

#### Post Doc:

Stefanie Zegowitz (financed by the Swedish Research Council)

Yiwei Zhang (visiting fellow). Since September 2015.

#### Research interests:

Low-dimensional dynamical systems and ergodic theory; mechanics of particles and systems; bifurcation theory.

#### Publications:

[1] Real 3x+1 (with M. Misiurewicz). Proc. of the Amer. Mathem. Soc. 133 (2005), 1109--1118.

[2] Secondary bifurcations in systems with all-to-all coupling. II. (with A.P.S. Dias), Dyn. Syst. 21 (2006), 439--463

[3] Double standard maps (with M. Misiurewicz). Commun. in Mathem. Phys. 273 (2007), 37--65.

[4] On the tip of the tongue (with M. Misiurewicz). J. of Fixed Point Th. and Applic. 3 (2008), 131--141.

[5] Hopf bifurcation with $S_n$ symmetry (with A.P.S.Dias). Nonlinearity 22 (2009), 627--666.

[6] 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.

[7] Kneading sequences for double standard maps (with M. Benedicks). Fund. Math. 206 (2009), 61--75.

[8] On the periodic orbits of Hamiltonian systems (with J. Llibre), J. Math. Phys. 51 (2010), 042704 12pp

[9] Non-generic cusps (with M. Misiurewicz). Trans. of the Amer. Mathem. Soc. 363 (2011), 3553--3572.

[10] Fixed points for positive permutation braids (with M. Misiurewicz). Fund. Math. 216 (2012), 129 -- 146

[11] Turning numbers for periodic orbits of disk homeomorphisms (with M. Misiurewicz). Journal of Fixed Point Theory and Applications , 13 (2013), 241--258.

[12] 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.

[13] On the limit cycles of the Floquet differential equations (with J. Llibre). Discrete and Continuous Dynamical Systems Ser. B 19 (2014), 1129--1136.

[14] Ergodicity of Avalanche Transformations (with M. Denker). Dynamical Systems 29 (2014), 517--536.

[15] A non-autonomous kind of Duffing equation (with J. Llibre). Applied Mathematics and Computation , 251 (2015), 669--674.

[16] Limit cycles of a class of Floquet differential equations (with J. Llibre). Submitted

[17] $\alpha$-standard maps. (with R. Ashton). Submitted

[18] 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.

[19] 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

[20] Hopf normal form with SN symmetry and reduction to systems of nonlinearly coupled phase oscillators (with P. Ashwin). Physica D: Nonlinear Phenomena Volume 325, 15 June 2016, Pages 14–24 Preprint version

[21] Chaos in generically coupled phase oscillator networks with nonpairwise interactions (with C. Bick and P. Ashwin). Chaos 26 (2016) 094814 Preprint version

[22] Counting preimages (with M. Misiurewicz). Ergod. Th. & Dynam. Sys. (posted electronically on January 24, 2017 Preprint version

[23] Fair measure and fair entropy for non Markov interval maps (with Y. Zhang). Stochastics and Dynamics. 17 (2017), no. 5, 1750035 Preprint version

[24] Embeddings of interval exchange transformations into planar piecewise isometries (with P. Ashwin, A. Goetz, P. Peres). Accepted for publication in Ergod. Th. & Dynam. Sys. Preprint version 2018

[25] On the dynamics of translated cone exchange transformations (with P. Peres). Preprint version 2018

[26] Fair measures for countable-to-one maps (with S. Roth and Z. Roth). Preprint version 2018

[27] Existence of non-trivial embeddings of interval exchange transformations into Piecewise Isometries (with P. Peres). Preprint version 2019

PhD Thesis: Bifurcations of Dynamical Systems with Symmetry. pdf University of Porto, November 2007.