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Academic Work |
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[1] |
D. Rochon, Sur
une généralisation des nombres complexes: les tétranombres,
Master's Thesis, Université de Montéal, 1997. |
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[2] |
D. Rochon,
Dynamique bicomplexe et théorème de Bloch pour fonctions
hyperholomorphes, Doctoral Thesis, Université de
Montréal, 2001. |
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Poetry |
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[1] |
M. Gorski & D. Rochon, L'ÉVEIL DU GRAND JOUR : Les chants tantriques de la théurgie fractale, ISBN 978-2-9817658-6-4,
Éditions de l'Exil, 2020. |
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Book Chapters |
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[1] |
K.S. Charak & D. Rochon, On Factorization of
Bicomplex Meromorphic Functions, Hypercomplex Analysis, Trends in Mathematics, Birkhäuser
Verlag Basel/Switzerland, 55-68 (2008). |
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[2] |
R. Gervais Lavoie & D. Rochon,
The Bicomplex Heisenberg Uncertainty Principle, Theoretical Concepts
of Quantum Mechanics, ISBN 978-953-51-0088-1,
InTech Book, 39-64 (2012). |
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Articles |
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[1] |
D. Rochon, A
Generalized Mandelbrot Set for Bicomplex Numbers, Fractals, 8, No. 4, 355-368 (2000). |
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[2] |
D. Rochon, A
Bloch Constant for Hyperholomorphic Functions, Complex
Variables, 44, 85-101 (2001). |
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[3] |
D. Rochon, On
a Generalized Fatou-Julia Theorem, Fractals, 11,
No. 3, 213-219 (2003). |
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[4] |
D. Rochon, A Bicomplex Riemann Zeta Function, Tokyo
Journal of Mathematics, 27, No. 2, 357-369 (2004). |
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[5] |
D. Rochon & S. Tremblay, Bicomplex Quantum Mechanics I: The Generalized Schrödinger Equation,
Advances in applied Clifford algebras, 14,
No. 2, 231-248 (2004). |
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[6] |
D. Rochon & M. Shapiro,
On algebraic properties of bicomplex and hyperbolic numbers,
Anal. Univ. Oradea, fasc. math., vol. 11 , 71-110 (2004). |
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[7] |
É. Martineau & D. Rochon, On a Bicomplex
Distance Estimation for the Tetrabrot, International Journal of
Bifurcation and Chaos, 15, No. 9, 3039-3050 (2005). |
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[8] |
D. Rochon & S. Tremblay,
Bicomplex Quantum Mechanics II: The Hilbert Space,
Advances in applied Clifford algebras, 16, No.
2, 135-157 (2006). |
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[9] |
D. Rochon,
On a relation of bicomplex pseudoanalytic function theory to the complexified
stationary Schrödinger equation, Complex Variables,
53, No. 6, 501-521 (2008). |
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[10] |
V. V. Kravchenko, D. Rochon & S. Tremblay,
On the Klein-Gordon equation and hyperbolic pseudoanalytic function
theory, J. Phys. A: Math. Theor., 41,
No. 6, 1-18 (2008). |
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[11] |
K.S. Charak, D. Rochon & N. Sharma,
Normal Families of Bicomplex Holomorphic Functions, Fractals,
17, No. 3, 257-268 (2009). |
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[12] |
V. Garant-Pelletier & D. Rochon,
On a generalized Fatou-Julia theorem in multicomplex spaces, Fractals, 17,
No. 3, 241-255 (2009). |
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[13] |
R. Gervais Lavoie, L. Marchildon & D. Rochon,
The Bicomplex Quantum Harmonic Oscillator, Nuovo Cimento B,
125, No. 10, 1173-1192 (2010). |
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[14] |
R. Gervais Lavoie, L. Marchildon & D. Rochon,
Infinite-Dimensional Bicomplex
Hilbert Spaces, Ann. Funct. Anal, 1,
No. 2, 75-91 (2010). |
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[15] |
R. Gervais Lavoie, L. Marchildon & D. Rochon,
Hilbert Space of the Bicomplex Quantum Harmonic Oscillator,
AIP Conference Proceedings, 1327, 148-157 (2011). |
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[16] |
R. Gervais Lavoie, L. Marchildon & D. Rochon,
Finite-Dimensional Bicomplex
Hilbert Spaces, Advances in applied Clifford algebras,
21, No. 3, 561-581 (2011). |
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[17] |
Rajeev Kumar, Romesh Kumar & D. Rochon, The
Fundamental Theorems in the framework of Bicomplex Topological Modules,
arXiv: 1109.3424 (2011). |
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[18] |
K.S. Charak, D. Rochon & N. Sharma, Normal
Families of Bicomplex Meromorphic Functions,
Annales Polonici Mathematici, 103, No. 3, 303-317 (2012). |
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[19] |
D. Rochon, Ravinder Kumar & K.S. Charak,
Bicomplex Riesz-Fischer Theorem, GJSFR,
13-F, No. 1, 67-77 (2013). |
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[20] |
K.S. Charak, Ravinder Kumar & D. Rochon, Infinite
Dimensional Bicomplex Spectral Decomposition Theorem, Advances
in applied Clifford algebras, 23, No. 3, 593-605
(2013). |
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[21] |
J. Mathieu, L. Marchildon & D. Rochon, The
Bicomplex Quantum Coulomb Potential Problem, Canadian Journal
of Physics, 91, 1193-1100 (2013). |
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[22] |
C. Matteau & D. Rochon,
The Inverse Iteration Method for Julia Sets in the 3-Dimensional Space, Chaos, Solitons & Fractals, 75, 272-280 (2015). |
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[23] |
P.-O. Parisé & D. Rochon, A Study of Dynamics of the Tricomplex Polynomial $\eta^p+c$, Nonlinear Dynamics, 82, 157-171 (2015). |
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[24] |
P.-O. Parisé, T. Ransford & D. Rochon,
Tricomplex Dynamical Systems Generated by Polynomials of Even Degree,
Chaotic Modeling and Simulation (CMSIM), 1, 37-48 (2017).
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[25] |
P.-O. Parisé & D. Rochon,
Tricomplex Dynamical Systems Generated by Polynomials of Odd Degree, Fractals, 25, No. 3, 1-11 (2017). |
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[26] |
G. Brouillette, P.-O. Parisé & D. Rochon,
Tricomplex Distance Estimation for Filled-in Julia Sets and Multibrot Sets, International Journal of
Bifurcation and Chaos, 29, No. 6 (2019). |
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[27] |
G. Brouillette & D. Rochon,
Characterization of the Principal 3D Slices Related to the Multicomplex Mandelbrot Set, Advances in applied Clifford algebras,
29, No. 39 (2019). |
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[28] |
A. Vallières & D. Rochon,
Relationship between the Mandelbrot Algorithm and the Platonic Solids, Mathematics,
10, No. 482 (2022). |
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[29] |
V. Boily & D. Rochon, On the Algebraic Foundation of the Mandelbulb,
Fractals, 31, No. 5 (2023). |
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