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Year: 2026
Type: other
Abstract: We prove componentwise upper bounds for Pollicott–Ruelle resonance counts in open hyperbolic flows. If a component trapped transversal has upper Minkowski dimension kappa_alpha and its invariant covector graph is C^{beta_alpha}, then N_alpha^cum(E, Gamma; a) <= C_{epsilon,Gamma,B} E^{1+kappa_alpha/(1+beta_alpha)+epsilon} uniformly on compact smooth control families. The proof combines an exact recurrent filtration of the intrinsic divisor with continuous Gaussian propagation, a finite-rank orthogonal Wilson absorber, and a signed-shell reduction on the matching trace space. We verify the criterion for smooth affine open suspensions with two recurrent horseshoes and a one-way wandering bridge. Reversing the bridge preserves the recurrent dynamics and full intrinsic divisor but changes the complete trapped-transversal dimension from 1 to 2 - 2delta. The componentwise packet exponent remains 3/2, whereas the unreduced whole-set exponent becomes 2 - delta.
Author: -
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170078235