Veselin Petkov - Academia.edu (original) (raw)
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Papers by Veselin Petkov
Nonlinearity, 2009
In this paper we prove two asymptotic estimates for pairs of closed trajectories for open billiar... more In this paper we prove two asymptotic estimates for pairs of closed trajectories for open billiards similar to those established by Pollicott and Sharp [PoS2] for closed geodesics on negatively curved compact surfaces. The first of these estimates holds for general open billiards in any dimension. The more intricate second estimate is established for open billiards satisfying the so called Dolgopyat type estimates. This class of billiards includes all open billiards in the plane and open billiards in R N (N ≥ 3) satisfying some additional conditions.
Communications in Mathematical Physics, 2000
In the general case of long-range trapping "black-box" perturbations we prove that the estimate o... more In the general case of long-range trapping "black-box" perturbations we prove that the estimate of the cut-o resolvent k (x)R(+i0) (x)k H!H C exp(Ch ?p); (x) 2 C 1 0 (R n); p 1 implies the estimate kR(+ i)k s;?s C 1 exp(C 1 h ?p).
Nonlinearity, 2009
In this paper we prove two asymptotic estimates for pairs of closed trajectories for open billiar... more In this paper we prove two asymptotic estimates for pairs of closed trajectories for open billiards similar to those established by Pollicott and Sharp [PoS2] for closed geodesics on negatively curved compact surfaces. The first of these estimates holds for general open billiards in any dimension. The more intricate second estimate is established for open billiards satisfying the so called Dolgopyat type estimates. This class of billiards includes all open billiards in the plane and open billiards in R N (N ≥ 3) satisfying some additional conditions.
Communications in Mathematical Physics, 2000
In the general case of long-range trapping "black-box" perturbations we prove that the estimate o... more In the general case of long-range trapping "black-box" perturbations we prove that the estimate of the cut-o resolvent k (x)R(+i0) (x)k H!H C exp(Ch ?p); (x) 2 C 1 0 (R n); p 1 implies the estimate kR(+ i)k s;?s C 1 exp(C 1 h ?p).