# Another Proof for the Existence of Dominated Splitting for Robustly Ergodic Diffeomorphisms

Volume 6, Issue 1, pp 13-17
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### Authors

Alireza Zamani Bahabadi - Department of Mathematics Ferdowsi University of Mashhad, Mashhad, Iran.

### Abstract

In this paper we show that any robustly ergodic system admits a dominated splitting without using pasting lemma for conservative diffeomorphisms .

### Share and Cite

##### ISRP Style

Alireza Zamani Bahabadi, Another Proof for the Existence of Dominated Splitting for Robustly Ergodic Diffeomorphisms, Journal of Mathematics and Computer Science, 6 (2013), no. 1, 13-17

##### AMA Style

Bahabadi Alireza Zamani, Another Proof for the Existence of Dominated Splitting for Robustly Ergodic Diffeomorphisms. J Math Comput SCI-JM. (2013); 6(1):13-17

##### Chicago/Turabian Style

Bahabadi, Alireza Zamani. "Another Proof for the Existence of Dominated Splitting for Robustly Ergodic Diffeomorphisms." Journal of Mathematics and Computer Science, 6, no. 1 (2013): 13-17

### Keywords

• Ergodic
• dominated splitting
• conservative diffeomorphism.

•  37C20
•  37C05
•  37C40
•  37D30

### References

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• [2] C. Bonatti, L. Diaz, E. Pujals, A $C^1$ -generic dichotomy for diffeomorphisms: Weak forms of hyperbolicity or infinitely many sinks or sources , Ann. Math. , 158 (2003), 355-418

• [3] C. Bonatti, N. Gourmelon, T. Vivier, Perturbations of the derivatives along periodic orbit, Ergodic Theory Dynam, systems, 26 (2006), 1307-1377

• [4] A. Tahzibi, Robust transitivity almost robust ergodicity, Ergodic Theory and Dynamical Systems, 24:4 (2004), 1261-1269

• [5] P. Zhang, Diffeomorphisms with global dominated splittings cannot be minimal, Proc. Am. Math. Soc., 140 (2012), 589 – 593