We show that the critical cusp exponent β = −1/2 admits W 2,1 invariant densities in anexplicit family of expanding full-branch interval maps. The usual estimates exclude this exponent becausetwo zero-order coefficients in the second derivative of the transfer operator are individually non-integrable.Their signed combination, however, contains the factor β(2β + 1) for a pure power cusp. We exploit itscancellation at β = −1/2 to prove a W 2,1 Lasota–Yorke inequality and a spectral gap for the explicit family.We also identify a separate obstruction caused by an interior cusp value. As an application, a small Bernoulliprobability perturbation between two fixed maps has a stationary density that depends real-analytically onthe perturbation parameter in W 2,1 , with explicit formulas for all response derivatives.
| Mualliflar | Oltiboev, Davrbek, Vafoyev, Furqat |
|---|---|
| Jurnal | Ўзбекистон Миллий университети хабарлари |
| Nashriyot | Ўзбекистон Миллий университети |
| ISSN | 2181-7324, 3093-8996 |
| Nashr sanasi | 2026-10-07 |
| Jild | 2 |
| Son | 2.3 |
| Betlar | 178-183 |
| Til | Ingliz |
| Indeksga qo‘shilgan | 2026-10-08 |
cusp maps, transfer operators, invariant density, Lasota–Yorke inequality, analytic response, random dynamical systems.
| APA | Oltiboev, Davrbek, & Vafoyev, Furqat (2026). Critical cusp cancellation and analytic response for a Bernoulli random interval map. Ўзбекистон Миллий университети хабарлари, 2(2.3), 178-183. https://journals.nuu.uz/index.php/actanuuz/article/view/15305 |
|---|---|
| GOST (OAK) | Oltiboev, Davrbek, Vafoyev, Furqat Critical cusp cancellation and analytic response for a Bernoulli random interval map // Ўзбекистон Миллий университети хабарлари. – 2026. – T. 2, № 2.3. – P. 178-183. |
| MLA | Oltiboev, Davrbek, and Vafoyev, Furqat. “Critical cusp cancellation and analytic response for a Bernoulli random interval map.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 178-183, 2026. https://journals.nuu.uz/index.php/actanuuz/article/view/15305 |
| Chicago | Oltiboev, Davrbek, and Vafoyev, Furqat. “Critical cusp cancellation and analytic response for a Bernoulli random interval map.” Ўзбекистон Миллий университети хабарлари, 2(2.3), 178-183 (2026). https://journals.nuu.uz/index.php/actanuuz/article/view/15305 |
| Harvard | Oltiboev, Davrbek, and Vafoyev, Furqat (2026) ‘Critical cusp cancellation and analytic response for a Bernoulli random interval map’, Ўзбекистон Миллий университети хабарлари, 2(2.3), 178-183. https://journals.nuu.uz/index.php/actanuuz/article/view/15305 |
| BibTeX | @article{oltiboevdavrbek2026,
title = {Critical cusp cancellation and analytic response for a Bernoulli random interval map},
author = {Oltiboev, Davrbek and Vafoyev, Furqat},
journal = {Ўзбекистон Миллий университети хабарлари},
year = {2026},
volume = {2},
number = {2.3},
pages = {178-183},
url = {https://journals.nuu.uz/index.php/actanuuz/article/view/15305}
} |
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