Publications
[1] D
rakopoulos V., On the additional fixed points of Schröder iteration functions associated with a
one-parameter family of cubic polynomials, Computers & Graphics 22 (1998), 629–634.
[3] Drakopoulos V., How is the
dynamics of König iteration functions affected by
their additional fixed points?,
Fractals 7 (1999), 327–334.
[4]
Drakopoulos V., Argyropoulos N. and Böhm A., Generalized
computation of Schröder iteration functions to
motivate families of Julia and Mandelbrot-like sets, SIAM Journal on Numerical
Analysis 36 (1999), 417–435.MR 2000d:65044
[5]
Drakopoulos V., Schröder
iteration functions associated with a one-parameter family of biquadratic
polynomials
, Chaos, Solitons & Fractals 13 (2002), 233
–243.
MR 2002g:37046
[7]
Drakopoulos
V., Kakos A. and
Nikolaou N., A probabilistic power domain algorithm for fractal image
decoding, Stochastics & Dynamics 2 (2002), 161–173. (DKN02)MR 2003b:68202
[8]
Drakopoulos V., Mimikou
Niki and Theoharis T., An overview of parallel visualisation methods for Mandelbrot and Julia sets,
Computers & Graphics 27 (2003), 635–646.
[9]
Dalla
Leoni, Drakopoulos V. and Prodromou Maria, On
the
box dimension for a class of nonaffine fractal
interpolation functions, Analysis in Theory and Applications 19 (2003), 220–233. (DDP03)MR 2004m:41007
[10]
Drakopoulos
V., Are there any Julia sets for the Laguerre iteration function?,
Computers & Mathematics with
Applications 46 (2003), 1201–1210. MR 2004i:37093
[12]
Bouboulis
P., Dalla
Leoni and Drakopoulos V., Image
compression using recurrent bivariate fractal interpolation surfaces,
International Journal of Bifurcation and Chaos 16 (7) (2006), 1–9. (BDD06)
[13]
Bouboulis
P., Dalla
Leoni and Drakopoulos V., Construction
of recurrent bivariate fractal interpolation surfaces and computation of their
box-counting dimension, Journal of Approximation Theory
141
(2006), 99
–
117
.
[18]
Drakopoulos
V., Sequential visualisation methods for the Mandelbrot set
,
Journal of Computational Methods in Sciences and Engineering 10 (1–2)(2010),
37–45.
[19]
Manousopoulos
P., Drakopoulos V. and Theoharis T., Parameter
identification of 1D recurrent fractal interpolation functions with
applications to imaging and signal processing, Journal of Mathematical
Imaging and Vision 40 (2) (2011), 162–170.
[20]
Drakopoulos V. and Manousopoulos P., Bivariate
fractal interpolation surfaces: Theory and applications,
International Journal of Bifurcation
and Chaos 22 (9) (2012), 1250220 [8 pages].
[21]
Alexopoulos C. and Drakopoulos V., On
the computation of the Kantorovich distance
for images, Chaotic Modeling and Simulation 2 (2012), 345–354.
[25]
Drakopoulos V. and Manousopoulos P., Non–tensor
product bivariate fractal interpolation surfaces on rectangular grids,
Constructive Approximation (submitted).
[26]
Drakopoulos
V., Manousopoulos P. And Theoharis T.,
Height field representation and compression using fractal
interpolation surfaces on rectangular domains
, EG UK Theory and Practice of Computer Graphics.
[27] Argyropoulos
N., Böhm A.
and Drakopoulos V., Julia and Mandelbrot-like sets for higher
order König iteration functions
, in Novak M. M. and Dewey T. G. (eds), Fractal frontiers, World Scientific,
Singapore, 1997, 169–178.
[28]
Drakopoulos
V. and Böhm A., Basins
of attraction and Julia sets of Schröder iteration functions, in Bountis T. and Pnevmatikos Sp. (eds), Order and Chaos in Nonlinear Dynamical
Systems,
Pnevmatikos,
[29]
Drakopoulos
V. and Dalla
Leoni, Space-filling curves generated by fractal interpolation functions,
in Iliev O. P., Kaschiev M.
S., Margenov S. D., Sendov Bl. H.and
Vassilevski P. S.
(eds), Recent
advances in numerical methods and applications ΙΙ, World Scientific,
Singapore, 1999, 784–792.
γ. Δημοσιεύσεις σε περιοδικά ή
επιστημονικές συλλογές χωρίς κριτές
[39]
Δάλλα
Λεώνη, Δρακόπουλος Β. και Μπεμ Αλ., Στοιχεία
από τη θεωρία των Fractals, Μαθηματική Επιθεώρηση 43 (1995), 21–48.
[40]
Δρακόπουλος
Β. και Ευαγγελάτου-Δάλλα
Λεώνη, Η νέα διάσταση της εκπαιδευτικής μαθηματικής σκέψης, 14ο Πανελλήνιο Συνέδριο Μαθηματικής Παιδείας, ΕΜΕ, 1997, 235–242.
[41]
Δρακόπουλος
Β. και Μπεμ Αλ., Η Γεωμετρία της Φύσης στην εκπαίδευση,
Διημερίδα Πληροφορικής «Η Πληροφορική στη
Δευτεροβάθμια Εκπαίδευση», ΕΠΥ, 1997, 117–124.
Theses, Dissertations and other publications
[45]
Δήμας Ευάγ. και Δρακόπουλος Β., Αριθμητική
επίλυση Μερικών Διαφορικών Εξισώσεων με τη μέθοδο των πεπερασμένων διαφορών,
εργασία που εκπονήθηκε στο Τμήμα Μαθηματικών του Πανεπιστημίου Αθηνών μέσα στα
πλαίσια του μαθήματος Αριθμητική Ανάλυση ΙΙ, 1989.
[48]
Δρακόπουλος
Β., Μελέτη
συνόλων τύπου
Juliaκαι Mandelbrotστον τετραδιάστατο χώρο των Quaternions
, Μεταδιδακτορική Διατριβή, Τμήμα Πληροφορικής και
Τηλεπικοινωνιών, Ε.Κ.Πανεπιστήμιο Αθηνών, 2000.
Citations (58)
2.
3.
Xavier Buff and Christian Henriksen,
On König’s root-finding algorithms
, Nonlinearity 16
: 989
–1015, 2003
στις
[2]
και
[21].
4.
Huojun
Ruan, Zhen Sha and Weiyi Su,
Counterexamples in
parameter identification problem of the fractal interpolation functions
, Journal of Approximation Theory 122
(1) :
121
–128, 2003
στην
[4]
.
5.
R
.
Huojun, S
.
Zhen
and
6.
Sergio Amat,
Sonia
Busquier
and
Sergio Plaza, Dynamics
of a family of third-order iterative methods that do not require using second
derivatives, A
pplied
Mathematics and Computation
154 (3): 735–746, 2004 στις [1], [3] και [5].
7.
Sergio Amat,
Sonia
Busquier
and
Sergio Plaza, Review
of some iterative root-finding methods from a dynamical point of view, Scientia10: 3
–35, 2004
στις
[3]
και
[21]
.
8.
Guohua
Jin and John Mellor-Crummey,
SFCGen
: A framework for efficient generation of
multi-dimensional space-filling curves, ACM
Transactions on Mathematical Software 31: 120–148, 2005 στην [25].
9.
Sergio Amat,
Sonia
Busquier
and
Sergio Plaza,
On the d
ynamics
of a family of third-order iterative
functions, ΑNZIAM Journal 48: 343–359, 2007 στην [21].
10.
Shou
Gang Sui and Shu Tang Liu, Control
of Julia sets, Chaos, Solitons and Fractals 26
(4):
1135–1147, 2005
στην
[5]
.
11.
Sergio Amat,
Sonia
Busquier
and
12.
Zheng
-shun Ruan and Xiao-Lin Wang, A
note on parameter identification problem for fractal interpolation functions,
Journal of Mathematics (Wuhan) 26,
no. 1, 63–66, 2006
στην
[4]
.
13.
Xingyuan
Wang and Xuejing Yu, Julia
sets for the standard Newton’s method, Halley’s method, and Schröder’s method, Applied Mathematics and Computation 189
(2):
1186–1195, 2007
στην
[1]
.
14.
Bouboulis
P. and Dalla
Leoni, Closed fractal interpolation surfaces, Journal of Mathematical
Analysis and Applications 327 (1):
116
–
126, 2007
στις
[4]
,
[12]
και
[13]
.
15.
Bouboulis
P. and Dalla
Leoni, Fractal interpolation surfaces derived from fractal interpolation
functions, Journal of Mathematical Analysis and Applications 336 (2): 919
–936, 2007
στην
[13]
.
16.
Bouboulis
P. and Dalla
Leoni, A general construction
of fractal interpolation
fun
ctions
on grids of
R
n
, European Journal of Applied Mathematics 18 (4): 449
–
476, 2007
στις
[10]
και
[13]
.
17.
Bouboulis
P., Pseudo random number
generation with the aid of iterated function systems on
R
2
,
International Journal of Modern Physics C
18 (5): 861
–
882, 2007
στην
[13]
.
18.
Xiancun
Chen, Qiuli
Guo and Lifeng X
i
, The range of an affine fractal
interpolation function
, International Journal of Nonlinear Science 3 (3): 181
–
186, 2007
στην
[4]
.
19.
Qin Wang, Min Jin and Lifeng Xi, Fitness of graph based on fractal
dimension, International Journal of Nonlinear Science 4 (2): 156
–
160, 2007
στην
[4]
.
20.
Jin
Min
, Wang Qin and Xi Lifeng, Optimization of affine fractal interpolation
function for graph fitness using genetic algorithms, 6th WSEAS International
Conference on E-ACTIVITIES,
21.
Xingyuan
Wang and
Tingting
Wang, Julia sets of generalized
22.
Min Jin, Qin Wang and Lifeng Xi, Investigation
on Fitting Graph Based on Fractal Dimension’s Pretreatment,
in B. Apolloni et al.
(eds), Knowledge-Based
Intelligent Information and Engineering Systems, LNCS 4693, Springer
–Verlag, Berlin and Heidelberg, 217–224, 2007
στην
[4]
.
23.
Qin Wang, Min Jin, Lifeng Xi and Zhaoling Meng
,
Fractal Interpolation Fitness Based on BOX
Dimension’s Pretreatment, in O. Castillo
et al. (eds), Theoretical
Advances and Applications of Fuzzy Logic and Soft Computing, ASC 42,
Springer–Verlag, Berlin and Heidelberg, 520–526, 2007
στην [4].
24.
Maria A. Navascues, Fractal interpolants on the unit circle, Applied Mathematics Letters 21: 366-371, 2008
στην
[4]
.
25.
S. Amat, C. Bermúdez, S. Busquier, S.
Plaza,
On the dynamics of the Euler iterative function
, Applied
Mathematics
and Computation197 (2): 725–732, 2008
στην
[21]
.
26.
Hong-Yong Wang
and
Xiu-Juan
Li,
Perturbation error
analysis for fractal interpolation functions and their moments
, Applied
Mathematics Letters
21
(5): 441–446, 2008 στην [4].
27.
Jin Min, Wang Qin and Xi Lifeng,
Research and
implementation on genetic algorithms for graph fitness optimization
,
WSEAS
TRANSACTIONS on SYSTEMS
7 (4): 321–331, 2008
στην
[4]
.
28.
Hong-Yong Wang, Shou-Zhi Yang and Xiu-Juan Li, Error analysis for bivariate fractal interpolation functions generated
by 3-D perturbed iterated function systems, Computers and Mathematics with
Applications 56: 1684–1692, 2008
στην
[13]
.
29.
Wolfgang Metzler and Chol
Hui Yun, Construction
of fractal interpolation surfaces on rectangular grids, International
Journal of Bifurcation and Chaos, 2008
στην
[13]
.
30.
Wolfgang Metzler and Chol
Hui Yun, Construction
of recurrent fractal interpolation surfaces (RFISs) on rectangular grids,
International Journal of Bifurcation and Chaos, 2008
στην
[13]
.
31.
Zhigang
Feng,
Variation and Minkowski dimension of fractal interpolation surface
, Journal
of Mathematical Analysis and Applications
345
(1): 322–334, 2008
στην
[13]
.
32.
Bouboulis
P., Dalla
Leoni and Kostaki-Kosta M.,
Construction of smooth fractal
surfaces using Hermite fractal interpolation
functions
,
Bull.
Greek
Math. Soc.
στην
[13]
.
33.
A.K.B. Chand and M.A. Navascués, Natural bicubic spline fractal interpolation
,
Nonlinear Analysis: Theory, Methods & Applications 69 (11):
3679–3691, 2008
στην
[12]
.
34.
W.
35.
Huo
-Jun Ruan, Wei-Yi Su and
Kui
Yao, Box dimension and fractional integral of
linear fractal interpolation functions,
Journal
of Approximation Theory
161 (1): 187–197 στην [4].
36.
ShiGuo
Lian,
Image authentication based on fractal features, Fractals 16 (4): 287–297,
2008 στην [14].
37.
Jin M. and Wang Q., Application of genetic algorithms in graph fitness from affine fractal
interpolation function, Journal of Information and Computational Science 5 (1): 351
–
358, 2008
στην
[4]
.
38.
Tang PP and Wang XH, An
iteration method with generally convergent
property for cubic polynomials, International Journal of Bifurcation and
Chaos 19 (1): 395
–
401 Jan 2009
στις
[3]
και
[9]
.
39.
Lian
ShiGuo, Chen X, Ye D.P, Secure
fractal image coding based on fractal parameter encryption, Fractals 17 (2): 149
–
160, Jun 2009
στην
[14]
.
40.
Wang, H.-Y., Sensitivity
analysis for hidden variable fractal interpolation functions and their moments
, Fractals
17 (2): 161
–
170, 2009
στην
[14]
.
41.
Wang, H.-Y., Error
estimates of fitting for bivariate fractal interpolation, Journal of
Mathematical Research & Exposition 29 (3): 551–557, May 2009
στην
[13]
.
42.
Coleman M. L., Niemann J. D.
and Jacobs E. P., Reconstruction of hillslope and valley paleotopography by application of a geomorphic model, Computers and Geosciences 35 (9): 1776
–
1784, 2009
στην
[13]
.
43.
Zhang Y.-P. and Fan Y.-J., Generalized synchronization of Julia sets, Kongzhi
Lilun Yu Yinyong/Control Theory and Applications 26 (4): 463
–
467, 2009
στην
[5]
.
44.
Hong-Yong Wang,
Jia
-Bing Ji and
Fei-Long Cao,
Surface fitting and error
analysis using fractal interpolation
, Journal of Computational and
Applied Mathematics
στις
[12]
,
[13]
και
[18]
.
[75]
Ευαγγελάτου
-Δάλλα Λ., Δρακόπουλος Β. και Μπουμπούλης
Παντ., Κατασκευή fractal επιφανειών
παρεμβολής και χρήση αυτών στη συμπίεση εικόνων, 10ο Πανελλήνιο Συνέδριο Μαθηματικής Ανάλυσης,
Αθήναι, Πολυτεχνειούπολη Ζωγράφου, 30 Σεπ. – 2 Οκτ.
2004.