Two-Dimensional Random Substitutions and Their Associated Dynamical Systems

Date of Award

12-1-2022

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

First Advisor

Eden Delight P. Miro, PhD

Abstract

I would like to express my profound gratitude and sincerest appreciation to my ever indefatigable adviser, Dr. Eden Delight P. Miro, for all the trust, support, understanding, and help she accorded me. I will be forever grateful for her benevolence - her tenacity to see that I will finish my degree even when it seems so bleak for me. Her incomparable guidance and immeasurable patience made it possible for me to complete this dissertation. I feel blessed and honored to have her as my adviser. I want to extend my sincere appreciation to my panel members, Dr. Alvaro Bustos- Gajardo, Dr. Jonathan V. Caalim, Dr. Job A. Nable, and Dr. Gwendolyn S. Tadeo, for their very insightful comments and suggestions that lead to the development of the study. Moreover, I also want to thank Dr. Dan Rust, whose research works have substantially influenced this study, and Dr. Neil Ma˜nibo, for the helpful discussion on digit substitutions. I am immensely indebted to the Department of Science and Technology - Science Education Institute (DOST-SEI) for the PhD scholarship grant, under the Accelerated Science and Technology Human Resource Development Program (ASTHRDP), which financially supported three years (6 semesters and 2 intersessions) of my stay in the PhD Mathematics program. If not for this opportunity, I would not dare pursue my graduate study at the Ateneo de Manila University. In addition, I am also beholden to the Office of the Associate Dean for Graduate Programs (OADGP) for granting me the Doctoral Scholarship for 1 semester and 1 intersession, after I have stopped receiving monthly stipend under my ASTHRDP scholarship. The financial support was greatly helpful as I was able to continue to work full time on my research and complete most of the research works. Now, I would like to take this opportunity to thank all the people who have given me the strength to move forward, helped me one way or another, or provided me with encouragement and love to finish my degree. My hearfelt gratitude to the following:

My classmates and friends, Kristan, Luis, and Mark, for being my constant support when we had our courseworks. Thank you so much for making my PhD journey fun, exciting, and colorful. To my highschool friends, Aira and Via, for sheltering me way back in 2016 when I was just applying for a masters degree and starting my graduate studies in Ateneo. I am so grateful for the utmost support you have given me. To my undergraduate professors, Ma’am Gwen, Ma’am Ia, Ma’am Laarni, and Ma’am Linda, for believing in me that I could finish my graduate studies in Ateneo. Thank you for all the words of encouragement. To the Felipe family, especially my cousins, for always checking on my well-being. I am overwhelmed by your eagerness to see me graduate. To my mother, Virginia L. Felipe, and my grandmother, Trinidad Layco, for their unconditional love and unfailing support to my every endeavor. I appreciate all your sacrifices to give me a space to do my research in our humble home. To my late father, Anacleto M. Felipe, for always being my guiding light. I am immensely grateful to you for letting me know the importance of education at a very young age. Above all others, to our Almighty GOD, for the blessings and delightful surprises. My deepest gratitude to the Almighty GOD for equipping me with an excellent arsenal of knowledge and wisdom to successfully complete this dissertation. THY will be done!

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