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Shadowing in linear skew product
Sergey TikhomirovAbstract
We consider linear skew product with the full shift in the base and non-zero Lyapunov exponent in the fiber. We provide sharp estimate for the precision of shadowing for a typical pseudotrajectory of finite length. This result suggests that the high-dimensional analogue of Hammel-Yorke-Grebogi's conjecture concerning the interval of shadowability for a typical pseudotrajectory is not correct. The main technique is reduction of shadowing problem to the ruin problem for one-dimensional random walk.
- Received:
- 30.10.14
- Published:
- 07.11.14
- MSC Codes:
- 37C50, 37D30, 60F10
- Keywords:
- Holder shadowing, skew product