Found 346 Documents (Results 1–100)
Numerical computation of the roots of Mandelbrot polynomials: an experimental analysis. (English) Zbl 1543.65067
Mandelbrot sets for fixed template iterations. (English) Zbl 1542.37030
Jha, Sangita (ed.) et al., Recent developments in fractal geometry and dynamical systems. AMS special session. Fractal geometry and dynamical systems, virtual, May 14–15, 2022. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 797, 1-14 (2024).
Generation of Mandelbrot and Julia sets for generalized rational maps using SP-iteration process equipped with \(s\)-convexity. (English) Zbl 1540.37063
Speiser meets Misiurewicz. (English) Zbl 1542.37039
Reviewer: Liangwen Liao (Nanjing)
Bifurcation for families of Ahlfors island maps. arXiv:2410.04180
Preprint, arXiv:2410.04180 [math.DS] (2024).
The boundedness locus and baby Mandelbrot sets for some generalized McMullen maps. (English) Zbl 07847396
Dynamics of Schwarz reflections: the mating phenomena. (Dynamique des réflexions de Schwarz: un phénomène d’accouplement.) (English. French summary) Zbl 1541.37046
First- and second-order framings of Mandelbrot sets and structure of fixed points of quadratic polynomials. (English. Russian original) Zbl 1531.30015
J. Math. Sci., New York 275, No. 4, 513-524 (2023); translation from Fundam. Prikl. Mat. 24, No. 2, 197-212 (2022).
MSC:
30D05
Analytic classification of generic unfoldings of antiholomorphic parabolic fixed points of codimension 1. (English) Zbl 1523.37056
Approximating roots by quadratic iteration. (English) Zbl 1531.37036
Reviewer: José Manuel Gutiérrez Jimenez (Logroño)
On the Mandelbrot set of \(z^p +\log c^t\) via the Mann and Picard-Mann iterations. (English) Zbl 1540.37065
Dynamical convergence of polynomials to products of power maps and the exponential. (English) Zbl 1521.37042
Reviewer: Yupin Wang (Jinan)
Newton-like components in the Chebyshev-Halley family of degree \(n\) polynomials. (English) Zbl 1518.37059
Reviewer: Patricia Dominguez (Puebla)
Mandelbrot and Julia sets of complex polynomials involving sine and cosine functions via Picard-Mann orbit. (English) Zbl 1526.37055
Dynamics of generalised exponential maps. (English) Zbl 1517.37054
Reviewer: Weiwei Cui (Lund)
Mirrors of conformal dynamics: Interplay between anti-rational maps, reflection groups, Schwarz reflections, and correspondences. arXiv:2310.03316
Preprint, arXiv:2310.03316 [math.DS] (2023).
Generic unfolding of an antiholomorphic parabolic point of codimension \(k\). arXiv:2301.11684
Preprint, arXiv:2301.11684 [math.DS] (2023).
Baker domains and non-convergent deformations. (English) Zbl 1507.37067
Reviewer: Tao Chen (New York)
A fractal eigenvector. (English) Zbl 1491.15012
Julia and Mandelbrot sets of transcendental function via Fibonacci-Mann iteration. (English) Zbl 1498.37076
Discontinuity of straightening in anti-holomorphic dynamics. II. (English) Zbl 1502.37055
Reviewer: Tao Chen (New York)
On the stochastic bifurcations regarding random iterations of polynomials of the form \(z^{2} + c_{n}\). arXiv:2206.06702
Preprint, arXiv:2206.06702 [math.DS] (2022).
Fixed point results of an implicit iterative scheme for fractal generations. (English) Zbl 1525.37045
Dynamics of two families of meromorphic functions involving hyperbolic cosine function. (English) Zbl 1482.37042
Rotation domains and stable Baker omitted value. (English) Zbl 1490.37061
Reviewer: Tao Chen (New York)
Discontinuity of straightening in anti-holomorphic dynamics. I. (English) Zbl 1487.37057
Reviewer: Walter Bergweiler (Kiel)
The Picard-Mann iteration with \(s\)-convexity in the generation of Mandelbrot and Julia sets. (English) Zbl 1477.37057
Reviewer: Walter Bergweiler (Kiel)
Invisible tricorns in real slices of rational maps. (English) Zbl 1466.37036
Reviewer: Shengyuan Zhao (Stony Brook)
Bifurcation loci of families of finite type meromorphic maps. arXiv:2107.02663
Preprint, arXiv:2107.02663 [math.DS] (2021).
The Parabolic Mandelbrot Set. arXiv:2107.09407
Preprint, arXiv:2107.09407 [math.DS] (2021).
The Mandelbrot set is the shadow of a Julia set. (English) Zbl 1457.37062
Reviewer: Luka Boc Thaler (Ljubljana)
Generalized Mandelbrot and Julia sets in a family of planar angle-doubling maps. (English) Zbl 1453.37040
Bohner, Martin (ed.) et al., Difference equations and discrete dynamical systems with applications. ICDEA 24, Dresden, Germany, May 21–25, 2018. Proceedings of the 24th international conference on difference equations and applications. Cham: Springer. Springer Proc. Math. Stat. 312, 21-54 (2020).
Reviewer: Tao Chen (New York)
The bifurcation measure has maximal entropy. (English) Zbl 1437.37061
Reviewer: Feng Rong (Shanghai)
Taylor coefficients of the conformal map for the exterior of the reciprocal of the multibrot set. (English) Zbl 1455.37043
Stability of Cantor Julia sets in the space of iterated elliptic functions. (English) Zbl 1430.37050
Hawkins, Jane (ed.) et al., Dynamical systems and random processes, 16th Carolina dynamics symposium, Agnes Scott College, Decatur, Georgia, April 13–15, 2018. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 736, 69-95 (2019).
Relating singularly perturbed rational maps to families of entire maps. (English) Zbl 1470.37070
Hawkins, Jane (ed.) et al., Dynamical systems and random processes, 16th Carolina dynamics symposium, Agnes Scott College, Decatur, Georgia, April 13–15, 2018. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 736, 49-68 (2019).
Reviewer: Walter Bergweiler (Kiel)
Lattès maps and the interior of the bifurcation locus. (English) Zbl 1433.37050
Reviewer: Jasna Prezelj (Ljubljana)
Misiurewicz parameters and dynamical stability of polynomial-like maps of large topological degree. (English) Zbl 1436.32069
Reviewer: Jasmin Raissy (Toulouse)
A distortion theorem for iterated inverse branches of holomorphic endomorphisms of \(\mathbb P^k\). (English) Zbl 1422.37031
Reviewer: Barbara Drinovec Drnovsek (Ljubljana)
A rigidity result for some parabolic germs. (English) Zbl 1405.37050
MSC:
37F45
30D05
Dynamics and Julia sets of iterated elliptic functions. (English) Zbl 1446.37049
Reviewer: Guoping Zhan (Hangzhou)
Linearization of quadratic polynomials according to Jean-Christophe Yoccoz (Linéarisation des polynômes quadratiques selon Jean-Christophe Yoccoz). (French) Zbl 1435.37070
Berger, Pierre (ed.) et al., Jean-Christophe Yoccoz. Conference on dynamical systems in memory of Jean-Christophe Yoccoz, Collège de France, Paris, France, May 29–31, 2017. Paris: Société Mathématique de France (SMF). Gaz. Math., Soc. Math. Fr., Spec. Iss., 36-66 (2018).
Attracting currents and equilibrium measures for quasi-attractors of \(\mathbb {P}^k\). (English) Zbl 1457.37064
Perturbations of examples of Lattès and Hausdorff dimension of bifurcation place. (Perturbations d’exemples de Lattès et dimension de Hausdorff du lieu de bifurcation.) (French. English summary) Zbl 1417.37171
Reviewer: Jasmin Raissy (Toulouse)
Stability and bifurcations in projective holomorphic dynamics. (English) Zbl 1407.32008
Przytycki, Feliks (ed.), Dynamical systems. Simons Semester in Banach Center, 2015. Papers based on the courses delivered at the Semester, Będlewo, Poland, September and November, 2015. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Cent. Publ. 115, 37-71 (2018).
Reviewer: Mohammad Sajid (Buraidah)
Antipode preserving cubic maps: the Fjord theorem. (English) Zbl 1390.37080
Reviewer: Walter Bergweiler (Kiel)
Repulsive cycles bifurcate in chains. (Les cycles répulsifs bifurquent en chaîne.) (French) Zbl 1388.32012
Semi-parabolic tools for hyperbolic Hénon maps and continuity of Julia sets in \(\mathbb {C}^{2}\). (English) Zbl 1385.37064
Schwarz reflections and the Tricorn. arXiv:1812.01573
Preprint, arXiv:1812.01573 [math.DS] (2018).
A complementary proof of Baker’s theorem of completely invariant components for transcendental entire functions. arXiv:1803.04598
Preprint, arXiv:1803.04598 [math.DS] (2018).
MSC:
30D05
37F45
Lower semi-continuity of entropy in a family of \(K3\) surface automorphisms. (English) Zbl 1397.14045
Antiholomorphic perturbations of Weierstrass zeta functions and Green’s function on tori. (English) Zbl 1378.37079
Reviewer: Tao Chen (Long Island City)
Bifurcations in the elementary desboves family. (English) Zbl 1375.32037
MSC:
32H50
37F45
Complex perspective for the projective heat map acting on pentagons. (English) Zbl 1381.37050
Reviewer: Marco Abate (Pisa)
Hausdorff dimension of biaccessible angles for quadratic polynomials. (English) Zbl 1375.37129
Reviewer: Mohammad Sajid (Buraidah)
Singular perturbations of Blaschke products and connectivity of Fatou components. (English) Zbl 1401.37055
Holomorphic endomorphisms of \(\mathbb{P}^{3}(\mathbb{C})\) related to a Lie algebra of type \(A_{3}\) and catastrophe theory. (English) Zbl 1380.37099
Reviewer: Jasmin Raissy (Toulouse)
Semi-parabolic bifurcations in complex dimension two. (English) Zbl 1365.37044
Reviewer: Feng Rong (Shanghai)
A study of the dynamics of the family \(f_{\lambda,\mu}=\lambda \sin z+\frac{\mu}{z-k\pi}\) where \(\lambda,\mu\in\mathbb{R}\setminus\{0\}\) and \(k\in\mathbb{Z}\setminus\{0\}\). (English) Zbl 1356.37063
MSC:
37F10
37F45
Domain of attraction for maps tangent to the identity in \(\mathbb C^2\) with characteristic direction of higher degree. (English) Zbl 1362.37091
Reviewer: Jesus Muciño-Raymundo (Morelia)
Equidistribution towards the bifurcation current. I: Multipliers and degree \(d\) polynomials. (English) Zbl 1380.37098
Reviewer: Marco Abate (Pisa)
Imaginary scators bound set under the iterated quadratic mapping in \(1+2\) dimensional parameter space. (English) Zbl 1334.37044
MSC:
37F45
Fatou coordinates for parabolic dynamics. (English) Zbl 1337.32006
Fornæss, John Erik (ed.) et al., Complex geometry and dynamics. The Abel symposium 2013, Trondheim, Norway, July 2–5, 2013. Cham: Springer (ISBN 978-3-319-20336-2/hbk; 978-3-319-20337-9/ebook). Abel Symposia 10, 259-270 (2015).
Convergence of rays with rational argument in hyperbolic components – an illustration in transcendental dynamics. (English) Zbl 1351.37188
Reviewer: Meirong Zhang (Beijing)
Hyperbolic components of McMullen maps. (Composantes hyperboliques des fractions de McMullen.) (English. French summary) Zbl 1327.30028
Reviewer: Tao Chen (Long Island City)
A remark on Zagier’s observation of the Mandelbrot set. (English) Zbl 1352.37142
Reviewer: Alexandre De Zotti (London)
Rescaling limits of complex rational maps. (English) Zbl 1347.37089
Reviewer: Alexandre De Zotti (London)
The \(M\)-set of \(\lambda \exp(z)/z\) has infinite area. (English) Zbl 1362.37094
Reviewer: Jasmin Raissy (Toulouse)
Unicritical Blaschke products and domains of ellipticity. (English) Zbl 1321.30017
Reviewer: José Manuel Gutiérrez Jimenez (Logrono)
Quadratic polynomials, multipliers and equidistribution. (English) Zbl 1334.37038
Reviewer: Walter Bergweiler (Kiel)
Holomorphic motion for Julia sets of holomorphic families of endomorphisms of CP(k). arXiv:1501.03454
Preprint, arXiv:1501.03454 [math.DS] (2015).
Collected papers of John Milnor. VII: Dynamical systems (1984–2012). Edited by Araceli Bonifant. (English) Zbl 1337.37002
Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-0937-1/hbk). xvi, 592 p. (2014).
Reviewer: Thomas B. Ward (Durham)
The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point. (English) Zbl 1351.37192
Invariants of holomorphic multidimensional discrete dynamic systems. (Russian. English summary) Zbl 1412.32016
MSC:
32H50
37F45
Explicit estimates on distance estimator method for Julia sets of polynomials. (English) Zbl 1291.37060
On the dynamics of a family of entire functions. (English) Zbl 1283.37053
Reviewer: Walter Bergweiler (Kiel)
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