• #### College of Science and Technology

• Email: warriaga@kean.edu

### Education background

Ph.D. (doctorate) mathematics.

M.Sc. and Diploma Civil mathematical engineer.
University of Chile, School of Engineers, Santiago, Chile.

Bachelor of sciences and engineering.
University of Chile, School of Engineers, Santiago, Chile.

### Courses teaching in WKU

MATH 1000  ALGEBRA FOR COLLEGE STUDENTS

MATH 1010  FOUNDATIONS OF MATH

### Biography

Dr. Waldo Arriagada is assistant professor of mathematics. He obtained his doctorate (mathematics) in the year 2010 by University of Montreal. During 2015-2021 he worked in the Department of Applied Mathematics of Khalifa University (UAE). He has held faculty positions at the University of The Bahamas (2013-2014) and at the Universidad Austral de Chile (2012). Waldo was postdoctoral fellow as well at the University of Calgary in the years 2010-2012. During this time, he published some results on the problem of isochrony and the equivalence of germs of elliptic unfoldings under conjugacy. He has some experience in finance and statistics as well. 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, called the Poincare monodromy, is well defined. 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 a more general setting which is 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. Hence, it is an exception rather than the general rule that singularities of these germs of analytic families unfoldings be normalizable.

### 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.
2. “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.
2. 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.
2. 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).
2. 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.
2. 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.
3. 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.
2. 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.
2. 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.
3. 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. 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)
2. 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)
3. Alkatheeri A. and Arriagada W. An algebraic note on Print Gallery.Applied Mathematics E-Notes (AMEN), No. 21 (2021), 669-677.