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Article cité :

On the geometry of period doubling invariant sets for area-preserving maps

Denis Gaidashev and Dan Lilja
Discrete and Continuous Dynamical Systems (2025)
https://doi.org/10.3934/dcds.2025082

Computer Experiments and Visualization in Mathematics and Physics: A Subjective Short Walk Among Some Historical Examples

J.-R. Chazottes and M. Monticelli
The Mathematical Intelligencer 45 (4) 320 (2023)
https://doi.org/10.1007/s00283-023-10313-2

Some elements for a history of the dynamical systems theory

Christophe Letellier, Ralph Abraham, Dima L. Shepelyansky, et al.
Chaos: An Interdisciplinary Journal of Nonlinear Science 31 (5) 053110 (2021)
https://doi.org/10.1063/5.0047851

Rigorous computer-assisted bounds on the period doubling renormalization fixed point and eigenfunctions in maps with critical point of degree 4

Andrew D. Burbanks, Andrew H. Osbaldestin and Judi A. Thurlby
Journal of Mathematical Physics 62 (11) (2021)
https://doi.org/10.1063/5.0054823

New Trends in One-Dimensional Dynamics

Edson de Faria, Peter Hazard and Charles Tresser
Springer Proceedings in Mathematics & Statistics, New Trends in One-Dimensional Dynamics 285 165 (2019)
https://doi.org/10.1007/978-3-030-16833-9_9

Propagation of a reaction front in a narrow sample of energetic material with heat losses: Chaotic regimes, extinction and intermittency

Vadim N. Kurdyumov and Vladimir V. Gubernov
Combustion and Flame 191 19 (2018)
https://doi.org/10.1016/j.combustflame.2018.01.003

Homoclinic-doubling and homoclinic-gluing bifurcations in the Takens-Bogdanov normal form with D4 symmetry

B. W. Qin, K. W. Chung, A. J. Rodríguez-Luis and M. Belhaq
Chaos: An Interdisciplinary Journal of Nonlinear Science 28 (9) (2018)
https://doi.org/10.1063/1.5030692

Innovation, dynamics and the myths about knowledge, technology and R&D-driven economic growth: an evolving network model

Hicham M. Hachem
Journal of Innovation Economics & Management n° 23 (2) 13 (2017)
https://doi.org/10.3917/jie.pr1.0011

Nested arithmetic progressions of oscillatory phases in Olsen's enzyme reaction model

Marcia R. Gallas and Jason A. C. Gallas
Chaos: An Interdisciplinary Journal of Nonlinear Science 25 (6) (2015)
https://doi.org/10.1063/1.4921178

Renormalization conjecture and rigidity theory for circle diffeomorphisms with breaks

Konstantin Khanin and Saša Kocić
Geometric and Functional Analysis 24 (6) 2002 (2014)
https://doi.org/10.1007/s00039-014-0309-0

Non-Single-Valley Solutions forp-Order Feigenbaum’s Type Functional Equationf(φ(x))=φp(f(x))

Min Zhang
Abstract and Applied Analysis 2014 1 (2014)
https://doi.org/10.1155/2014/731863

Infinite Feigenbaum sequences and spirals in the vicinity of the Lagrangian periodic solutions

Antonis D. Pinotsis
Celestial Mechanics and Dynamical Astronomy 108 (2) 187 (2010)
https://doi.org/10.1007/s10569-010-9294-2

Dynamics and Universality of Unimodal Mappings with Infinite Criticality

Genadi Levin and Grzegorz Światek
Communications in Mathematical Physics 258 (1) 103 (2005)
https://doi.org/10.1007/s00220-005-1333-6

Lyapunov exponents, dual Lyapunov exponents, and multifractal analysis

Aihua Fan and Yunping Jiang
Chaos: An Interdisciplinary Journal of Nonlinear Science 9 (4) 849 (1999)
https://doi.org/10.1063/1.166468

Fine structure and complex exponents in power-law distributions from random maps

Per Jögi, Didier Sornette and Michael Blank
Physical Review E 57 (1) 120 (1998)
https://doi.org/10.1103/PhysRevE.57.120

Infinitely renormalizable diffeomorphisms of the disk at the boundary of chaos

Eleonora Catsigeras, Jean-Marc Gambaudo and Fernando Moreira
Proceedings of the American Mathematical Society 126 (1) 297 (1998)
https://doi.org/10.1090/S0002-9939-98-03945-8

From one-dimensional to infinite-dimensional dynamical systems: Ideal turbulence

E. Yu. Romanenko and A. N. Sharkovsky
Ukrainian Mathematical Journal 48 (12) 1817 (1996)
https://doi.org/10.1007/BF02375370

Wavelet analysis and applications to some dynamical systems

Ph. Bendjoya and E. Slezak
Celestial Mechanics and Dynamical Astronomy 56 (1-2) 231 (1993)
https://doi.org/10.1007/BF00699735

From quasiperiodicity to chaos in the Belousov–Zhabotinskii reaction. I. Experiment

F. Argoul, A. Arneodo, P. Richetti and J. C. Roux
The Journal of Chemical Physics 86 (6) 3325 (1987)
https://doi.org/10.1063/1.452751

A crisis in the Belousov-Zhabotinskii reaction: Experiment and simulation

P. Richetti, P. De Kepper, J. C. Roux and Harry L. Swinney
Journal of Statistical Physics 48 (5-6) 977 (1987)
https://doi.org/10.1007/BF01009527

From quasiperiodicity to chaos in the Belousov–Zhabotinskii reaction. II. Modeling and theory

P. Richetti, J. C. Roux, F. Argoul and A. Arneodo
The Journal of Chemical Physics 86 (6) 3339 (1987)
https://doi.org/10.1063/1.451992

A parameter renormalization for orbit-splittings and band-mergings of iterated maps of an interval

Ky�z� Takeyama
Zeitschrift f�r Physik B Condensed Matter 52 (3) 253 (1983)
https://doi.org/10.1007/BF01307377