• ### Assistant Professor

• #### College of Science and Technology

• Email: warriaga@kean.edu

### Education background

Ph.D. (doctorate) Applied Mathematics.

University of Chile, Chile.

M.Sc. and Diploma Civil Mathematical Engineer.

University of Chile, Santiago, Chile.

BSc and engineering.

### Courses teaching in WKU

Calculus

Algebra for College Students

Foundations of Math

### Biography

Dr. Waldo Arriagada is assistant professor of mathematics. He obtained his doctorate (mathematics) in  2010 by University of Montreal. During 2015-2021 he was appointed Assistant Professor in the Department of Mathematics at Khalifa University (UAE). He has held faculty positions at the University of The Bahamas (2013-2014) and Universidad Austral de Chile (2012). Waldo was postdoctoral fellow at the University of Calgary during 2010-2012. He has published some results on the problem of isochrony and the equivalence of germs of elliptic unfoldings under conjugacy. In November 2021, Waldo gained an International Academic Qualifications certification by World Educational Services (USA). He is member of the Public Service Alliance of Canada (PSAC) and in 2012 he was nominated Maître de Conférences by the French Government.

### Research interests

His research interests include:

• partial and ordinary differential equations
• complex and holomorphic geometry

One aspect of these topics concerns the study of the geometrical methods involved in the characterization of the orbit space of a singular holomorphic (complex) foliation. It is known that this kind of foliations are sometimes uniquely defined by the germ of a self-map (the Poincare monodromy). The question whether the germ of the monodromy defines the analytic class of the real foliation under orbital equivalence follows naturally. These problems belong to the study of equilibria of parameter-dependent analytic dynamical systems (or unfoldings) and the identification of a complete set of invariants under analytical equivalence. The corresponding moduli space is dramatically huge, as already noticed by Il’Yashenko and his school in the 1980’s.

### Selected publications

Monographs

1. “Characterization of the unfolding of a weak focus and modulus of analytic classification”, Papyrus, University of Montreal, Montreal, Quebec, December 2010.

1. “Topological asymptotic linking number of solenoids embedded in the solid torus”, University of Chile, Santiago de Chile, December 2005.

Peer reviewed Scopus/WOS papers

2011

1. Arriagada W. and Rousseau C. The modulus of analytic classification for the unfolding of the codimension-one flip and Hopf bifurcations.Ann. Fac.Sc. Toulouse, Vol. 20, No. 3, pp. 541- 580, 2011.

2012

1. Arriagada W. Characterization of the generic unfolding of a weak focus. J. Diff. Eqs., 253, No. 6, pp. 1692- 1708, 2012.

2013

1. Arriagada W. Analytic obstructions to isochronicity in codimension 1. Proc. A Royal Soc. Edinburgh, 143, No. 4, pp. 669-688,2013.

1. Arriagada W. and Huentutripay J. Embedding of the codimension-k flip bifurcation. F. East. Jour. Dyn. Syst., 22, No. 1, pp. 33-54, 2013.

2014

1. Arriagada, W. and Huentutripay J. Blow-up rates of large solutions for a phi-Laplacian problem with gradient term. Proc. A Royal Soc. Edinburgh, 144, No. 1, pp. 1-21, 2014.

1. Arriagada W. Temporally normalizable generic unfoldings of order-1 weak foci. J. Dyn. and Cont. Systems, Volume 21, Issue 2 (2014), Pages 239-256.

2015

1. Arriagada W.and Ramirez H. Centers of skew-polynomial rings.Pub. Inst. Math. Beograde, Nouvelle Serie, Vol. 97(111), 181-186 (2015).

1. Arriagada W. Linking invariants for smooth minimal solenoids. Dyn. Systems, Vol. 30, No. 03, 297-309, 2015.

2016

1. Arriagada W.and Fialho J.Parametric rigidness of germs of analytic unfoldings with a Hopf bifurcation. Portugaliae Mathematica, European Mathematical Society, Vol. 73, Fasc. 2, 2016, 153–170.

2017

1. Arriagada W.and Huentutripay J. Characterization of a homogeneous Orlicz space. Electron. J. Differential Equations, Vol. 2017 (2017), No. 49, pp. 1–17.

1. Arriagada W.and Huentutripay J. Regularity, positivity and asymptotic vanishing of solutions of a φ-Laplacian. Anal. St. Univ. Ovidius Constanta, Ser. Mat., Vol. 25(3), 2017, 59–72.

1. Arriagada W.and Ramirez H. A note on involutions in Ore extensions. Boletin de Matematicas, 24, No. 1, 29-35, 2017.

2018

1. Arriagada W.and Huentutripay J. A Harnack’s inequality in Orlicz-Sobolev spaces. Studia Mathematica 243 (2018) , 117-137.

1. Arriagada W and J. Huentutripay. Improved bounds for solutions of $\phi$-Laplacians.Opuscula Math. 38, no. 6 (2018), 765-777.

2019

1. Arriagada W.and Huentutripay J. Existence and local boundedness of solutions of a φ-Laplacian problem. Applicable Analysis, 98, no. 4, 2019, 667-681.

1. Arriagada W.Parametric rigidity of real families of conformal diffeomorphisms tangent to x–> -x.Proceedings of the Royal Society of Edinburgh, Vol. 149, No. 1, 261–277, 2019.

1. Arriagada W and Skrzypacz P. Z2-equivariant foliations.Revue Roumaine de Mathematiques Pures et Appliquees (Romanian Journal of Pure and Applied Mathematics), Tome LXIV (2019), No.1, 7-24.

2020

1. Arriagada W and J. Huentutripay. Asymptotic properties of a φ-Laplacian and Rayleigh quotient.Comment.Math.Univ.Carolin. 61,3 (2020) 345-362.

2021

1. 19. Arriagada W.Matuszewska-Orlicz indices of the Sobolev conjugate Young function, Diff. Eqs. in Applied Mathematics, Elsevier, Volume 3, June 2021, 100029, 2021. (Available online at https://www.sciencedirect.com/science/article/pii/S2666818121000097)

1. Alkatheeri A. and Arriagada W. An algebraic note on Print Gallery.Applied Mathematics E-Notes (AMEN), No. 21 (2021), 669-677.

2022

1. Arriagada W.Parametric rigidness of the Hopf bifurcation up to analytic conjugacy. Periodica Mathematica Hungarica,2021. (Available online at https://doi.org/10.1007/s10998-021-00385-y)

Submitted

1. Arriagada W.Convergence properties of a φ-Laplacian under natural constraints, 2022.

In preparation

1. Arriagada W. and Huentutripay J. A classof φ-Laplacians with Caratheodory right-hand side.

1. Arriagada W. and Hameed R. A note on Polarizations and the Gram matrix.