# American Institute of Mathematical Sciences

November  2003, 9(6): 1361-1386. doi: 10.3934/dcds.2003.9.1361

## Sustainable dynamical systems

 1 Department of Mathematics, University of Michigan, East Hall 525, East University Avenue, Ann Arbor, MI 48109-1109, United States

Received  July 2002 Revised  August 2003 Published  September 2003

In this paper we investigate randomly perturbed orbits. If a dynamical system is hyperbolic one can keep random perturbations from accumulating into large deviations by making small corrections. We study the converse problem. This leads naturally to the notion of sustainable orbits.
Citation: John Erik Fornæss. Sustainable dynamical systems. Discrete & Continuous Dynamical Systems - A, 2003, 9 (6) : 1361-1386. doi: 10.3934/dcds.2003.9.1361
 [1] Meiyu Su. True laminations for complex Hènon maps. Conference Publications, 2003, 2003 (Special) : 834-841. doi: 10.3934/proc.2003.2003.834 [2] Shmuel Friedland, Gunter Ochs. Hausdorff dimension, strong hyperbolicity and complex dynamics. Discrete & Continuous Dynamical Systems - A, 1998, 4 (3) : 405-430. doi: 10.3934/dcds.1998.4.405 [3] Xu Zhang, Guanrong Chen. Polynomial maps with hidden complex dynamics. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2941-2954. doi: 10.3934/dcdsb.2018293 [4] Suzanne Lynch Hruska. Rigorous numerical models for the dynamics of complex Hénon mappings on their chain recurrent sets. Discrete & Continuous Dynamical Systems - A, 2006, 15 (2) : 529-558. doi: 10.3934/dcds.2006.15.529 [5] Tien-Cuong Dinh, Nessim Sibony. Rigidity of Julia sets for Hénon type maps. Journal of Modern Dynamics, 2014, 8 (3&4) : 499-548. doi: 10.3934/jmd.2014.8.499 [6] Karla Díaz-Ordaz. Decay of correlations for non-Hölder observables for one-dimensional expanding Lorenz-like maps. Discrete & Continuous Dynamical Systems - A, 2006, 15 (1) : 159-176. doi: 10.3934/dcds.2006.15.159 [7] Feng Zhou, Chunyou Sun. Dynamics for the complex Ginzburg-Landau equation on non-cylindrical domains I: The diffeomorphism case. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3767-3792. doi: 10.3934/dcdsb.2016120 [8] Dawei Yang, Shaobo Gan, Lan Wen. Minimal non-hyperbolicity and index-completeness. Discrete & Continuous Dynamical Systems - A, 2009, 25 (4) : 1349-1366. doi: 10.3934/dcds.2009.25.1349 [9] Yakov Pesin, Vaughn Climenhaga. Open problems in the theory of non-uniform hyperbolicity. Discrete & Continuous Dynamical Systems - A, 2010, 27 (2) : 589-607. doi: 10.3934/dcds.2010.27.589 [10] Hans Koch. On hyperbolicity in the renormalization of near-critical area-preserving maps. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 7029-7056. doi: 10.3934/dcds.2016106 [11] Bastian Laubner, Dierk Schleicher, Vlad Vicol. A combinatorial classification of postsingularly finite complex exponential maps. Discrete & Continuous Dynamical Systems - A, 2008, 22 (3) : 663-682. doi: 10.3934/dcds.2008.22.663 [12] Lluís Alsedà, David Juher, Pere Mumbrú. Minimal dynamics for tree maps. Discrete & Continuous Dynamical Systems - A, 2008, 20 (3) : 511-541. doi: 10.3934/dcds.2008.20.511 [13] Carlos Correia Ramos, Nuno Martins, Paulo R. Pinto. Escape dynamics for interval maps. Discrete & Continuous Dynamical Systems - A, 2019, 39 (11) : 6241-6260. doi: 10.3934/dcds.2019272 [14] Jianghong Bao. Complex dynamics in the segmented disc dynamo. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3301-3314. doi: 10.3934/dcdsb.2016098 [15] TÔn Vı$\underset{.}{\overset{\hat{\ }}{\mathop{\text{E}}}}\,$T T$\mathop {\text{A}}\limits_.$, Linhthi hoai Nguyen, Atsushi Yagi. A sustainability condition for stochastic forest model. Communications on Pure & Applied Analysis, 2017, 16 (2) : 699-718. doi: 10.3934/cpaa.2017034 [16] Cezar Joiţa, William O. Nowell, Pantelimon Stănică. Chaotic dynamics of some rational maps. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 363-375. doi: 10.3934/dcds.2005.12.363 [17] Paweł Góra, Abraham Boyarsky, Zhenyang LI, Harald Proppe. Statistical and deterministic dynamics of maps with memory. Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4347-4378. doi: 10.3934/dcds.2017186 [18] Begoña Alarcón, Sofia B. S. D. Castro, Isabel S. Labouriau. Global dynamics for symmetric planar maps. Discrete & Continuous Dynamical Systems - A, 2013, 33 (6) : 2241-2251. doi: 10.3934/dcds.2013.33.2241 [19] Eugen Mihailescu. Unstable manifolds and Hölder structures associated with noninvertible maps. Discrete & Continuous Dynamical Systems - A, 2006, 14 (3) : 419-446. doi: 10.3934/dcds.2006.14.419 [20] Vincent Lynch. Decay of correlations for non-Hölder observables. Discrete & Continuous Dynamical Systems - A, 2006, 16 (1) : 19-46. doi: 10.3934/dcds.2006.16.19

2018 Impact Factor: 1.143