---
_id: '8525'
abstract:
- lang: eng
  text: Let M be a smooth compact manifold of dimension at least 2 and Diffr(M) be
    the space of C r smooth diffeomorphisms of M. Associate to each diffeomorphism
    f;isin; Diffr(M) the sequence P n (f) of the number of isolated periodic points
    for f of period n. In this paper we exhibit an open set N in the space of diffeomorphisms
    Diffr(M) such for a Baire generic diffeomorphism f∈N the number of periodic points
    P n f grows with a period n faster than any following sequence of numbers {a n
    } n ∈ Z + along a subsequence, i.e. P n (f)>a ni for some n i →∞ with i→∞. In
    the cases of surface diffeomorphisms, i.e. dim M≡2, an open set N with a supergrowth
    of the number of periodic points is a Newhouse domain. A proof of the man result
    is based on the Gontchenko–Shilnikov–Turaev Theorem [GST]. A complete proof of
    that theorem is also presented.
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
  full_name: Kaloshin, Vadim
  id: FE553552-CDE8-11E9-B324-C0EBE5697425
  last_name: Kaloshin
  orcid: 0000-0002-6051-2628
citation:
  ama: Kaloshin V. Generic diffeomorphisms with superexponential growth of number
    of periodic orbits. <i>Communications in Mathematical Physics</i>. 2000;211:253-271.
    doi:<a href="https://doi.org/10.1007/s002200050811">10.1007/s002200050811</a>
  apa: Kaloshin, V. (2000). Generic diffeomorphisms with superexponential growth of
    number of periodic orbits. <i>Communications in Mathematical Physics</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s002200050811">https://doi.org/10.1007/s002200050811</a>
  chicago: Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth
    of Number of Periodic Orbits.” <i>Communications in Mathematical Physics</i>.
    Springer Nature, 2000. <a href="https://doi.org/10.1007/s002200050811">https://doi.org/10.1007/s002200050811</a>.
  ieee: V. Kaloshin, “Generic diffeomorphisms with superexponential growth of number
    of periodic orbits,” <i>Communications in Mathematical Physics</i>, vol. 211.
    Springer Nature, pp. 253–271, 2000.
  ista: Kaloshin V. 2000. Generic diffeomorphisms with superexponential growth of
    number of periodic orbits. Communications in Mathematical Physics. 211, 253–271.
  mla: Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number
    of Periodic Orbits.” <i>Communications in Mathematical Physics</i>, vol. 211,
    Springer Nature, 2000, pp. 253–71, doi:<a href="https://doi.org/10.1007/s002200050811">10.1007/s002200050811</a>.
  short: V. Kaloshin, Communications in Mathematical Physics 211 (2000) 253–271.
date_created: 2020-09-18T10:50:20Z
date_published: 2000-04-01T00:00:00Z
date_updated: 2021-01-12T08:19:52Z
day: '01'
doi: 10.1007/s002200050811
extern: '1'
intvolume: '       211'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '04'
oa_version: None
page: 253-271
publication: Communications in Mathematical Physics
publication_identifier:
  issn:
  - 0010-3616
  - 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Generic diffeomorphisms with superexponential growth of number of periodic
  orbits
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 211
year: '2000'
...
---
_id: '2729'
abstract:
- lang: eng
  text: We give the leading order semiclassical asymptotics for the sum of the negative
    eigenvalues of the Pauli operator (in dimension two and three) with a strong non-homogeneous
    magnetic field. As in [LSY-II] for homogeneous field, this result can be used
    to prove that the magnetic Thomas-Fermi theory gives the leading order ground
    state energy of large atoms. We develop a new localization scheme well suited
    to the anisotropic character of the strong magnetic field. We also use the basic
    Lieb-Thirring estimate obtained in our companion paper [ES-I].
acknowledgement: L. E. gratefully acknowledges financial support from the Forschungsinstitut
  fur Mathematik, ETH, Zurich, where this work was started. He is also grateful for
  the hospitality and support of Aarhus University during his visits. The authors
  wish to thank the referee for the careful reading of the manuscript and the many
  helpful remarks and suggestions.
article_processing_charge: No
article_type: original
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Jan
  full_name: Solovej, Jan
  last_name: Solovej
citation:
  ama: Erdös L, Solovej J. Semiclassical eigenvalue estimates for the Pauli operator
    with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates.
    <i>Communications in Mathematical Physics</i>. 1997;188(3):599-656. doi:<a href="https://doi.org/10.1007/s002200050181">10.1007/s002200050181</a>
  apa: Erdös, L., &#38; Solovej, J. (1997). Semiclassical eigenvalue estimates for
    the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order
    asymptotic estimates. <i>Communications in Mathematical Physics</i>. Springer.
    <a href="https://doi.org/10.1007/s002200050181">https://doi.org/10.1007/s002200050181</a>
  chicago: Erdös, László, and Jan Solovej. “Semiclassical Eigenvalue Estimates for
    the Pauli Operator with Strong Non-Homogeneous Magnetic Fields, II. Leading Order
    Asymptotic Estimates.” <i>Communications in Mathematical Physics</i>. Springer,
    1997. <a href="https://doi.org/10.1007/s002200050181">https://doi.org/10.1007/s002200050181</a>.
  ieee: L. Erdös and J. Solovej, “Semiclassical eigenvalue estimates for the Pauli
    operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic
    estimates,” <i>Communications in Mathematical Physics</i>, vol. 188, no. 3. Springer,
    pp. 599–656, 1997.
  ista: Erdös L, Solovej J. 1997. Semiclassical eigenvalue estimates for the Pauli
    operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic
    estimates. Communications in Mathematical Physics. 188(3), 599–656.
  mla: Erdös, László, and Jan Solovej. “Semiclassical Eigenvalue Estimates for the
    Pauli Operator with Strong Non-Homogeneous Magnetic Fields, II. Leading Order
    Asymptotic Estimates.” <i>Communications in Mathematical Physics</i>, vol. 188,
    no. 3, Springer, 1997, pp. 599–656, doi:<a href="https://doi.org/10.1007/s002200050181">10.1007/s002200050181</a>.
  short: L. Erdös, J. Solovej, Communications in Mathematical Physics 188 (1997) 599–656.
date_created: 2018-12-11T11:59:18Z
date_published: 1997-10-01T00:00:00Z
date_updated: 2022-08-22T09:25:09Z
day: '01'
doi: 10.1007/s002200050181
extern: '1'
intvolume: '       188'
issue: '3'
language:
- iso: eng
month: '10'
oa_version: None
page: 599 - 656
publication: Communications in Mathematical Physics
publication_identifier:
  issn:
  - 0010-3616
publication_status: published
publisher: Springer
publist_id: '4164'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous
  magnetic fields, II. Leading order asymptotic estimates
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 188
year: '1997'
...
---
_id: '2724'
abstract:
- lang: eng
  text: We study the generalizations of the well-known Lieb-Thirring inequality for
    the magnetic Schrödinger operator with nonconstant magnetic field. Our main result
    is the naturally expected magnetic Lieb-Thirring estimate on the moments of the
    negative eigenvalues for a certain class of magnetic fields (including even some
    unbounded ones). We develop a localization technique in path space of the stochastic
    Feynman-Kac representation of the heat kernel which effectively estimates the
    oscillatory effect due to the magnetic phase factor.
article_processing_charge: No
article_type: original
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
citation:
  ama: Erdös L. Magnetic Lieb-Thirring inequalities. <i>Communications in Mathematical
    Physics</i>. 1995;170(3):629-668. doi:<a href="https://doi.org/10.1007/BF02099152">10.1007/BF02099152</a>
  apa: Erdös, L. (1995). Magnetic Lieb-Thirring inequalities. <i>Communications in
    Mathematical Physics</i>. Springer. <a href="https://doi.org/10.1007/BF02099152">https://doi.org/10.1007/BF02099152</a>
  chicago: Erdös, László. “Magnetic Lieb-Thirring Inequalities.” <i>Communications
    in Mathematical Physics</i>. Springer, 1995. <a href="https://doi.org/10.1007/BF02099152">https://doi.org/10.1007/BF02099152</a>.
  ieee: L. Erdös, “Magnetic Lieb-Thirring inequalities,” <i>Communications in Mathematical
    Physics</i>, vol. 170, no. 3. Springer, pp. 629–668, 1995.
  ista: Erdös L. 1995. Magnetic Lieb-Thirring inequalities. Communications in Mathematical
    Physics. 170(3), 629–668.
  mla: Erdös, László. “Magnetic Lieb-Thirring Inequalities.” <i>Communications in
    Mathematical Physics</i>, vol. 170, no. 3, Springer, 1995, pp. 629–68, doi:<a
    href="https://doi.org/10.1007/BF02099152">10.1007/BF02099152</a>.
  short: L. Erdös, Communications in Mathematical Physics 170 (1995) 629–668.
date_created: 2018-12-11T11:59:16Z
date_published: 1995-06-01T00:00:00Z
date_updated: 2022-06-28T09:19:36Z
day: '01'
doi: 10.1007/BF02099152
extern: '1'
intvolume: '       170'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007/BF02099152
month: '06'
oa_version: None
page: 629 - 668
publication: Communications in Mathematical Physics
publication_identifier:
  issn:
  - 0010-3616
publication_status: published
publisher: Springer
publist_id: '4168'
quality_controlled: '1'
status: public
title: Magnetic Lieb-Thirring inequalities
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 170
year: '1995'
...
---
_id: '2722'
abstract:
- lang: eng
  text: 'A version of the one-dimensional Rayleigh gas is considered: a point particle
    of mass M (molecule), confined to the unit interval [0,1], is surrounded by an
    infinite ideal gas of point particles of mass 1 (atoms). The molecule interacts
    with the atoms and with the walls via elastic collision. Central limit theorems
    are proved for a wide class of additive functionals of this system (e.g. the number
    of collisions with the walls and the total length of the molecular path).'
acknowledgement: "The authors are very grateful to D. Szasz and A. Kramli for valuable
  discussions and their encouragement. We are also indebted to D. Dϋrr for his comments
  and suggestions.\r\n"
article_processing_charge: No
article_type: original
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Dao
  full_name: Tuyen, Dao
  last_name: Tuyen
citation:
  ama: Erdös L, Tuyen D. Central limit theorems for the one-dimensional Rayleigh gas
    with semipermeable barriers. <i>Communications in Mathematical Physics</i>. 1992;143(3):451-466.
    doi:<a href="https://doi.org/10.1007/BF02099260">10.1007/BF02099260</a>
  apa: Erdös, L., &#38; Tuyen, D. (1992). Central limit theorems for the one-dimensional
    Rayleigh gas with semipermeable barriers. <i>Communications in Mathematical Physics</i>.
    Springer. <a href="https://doi.org/10.1007/BF02099260">https://doi.org/10.1007/BF02099260</a>
  chicago: Erdös, László, and Dao Tuyen. “Central Limit Theorems for the One-Dimensional
    Rayleigh Gas with Semipermeable Barriers.” <i>Communications in Mathematical Physics</i>.
    Springer, 1992. <a href="https://doi.org/10.1007/BF02099260">https://doi.org/10.1007/BF02099260</a>.
  ieee: L. Erdös and D. Tuyen, “Central limit theorems for the one-dimensional Rayleigh
    gas with semipermeable barriers,” <i>Communications in Mathematical Physics</i>,
    vol. 143, no. 3. Springer, pp. 451–466, 1992.
  ista: Erdös L, Tuyen D. 1992. Central limit theorems for the one-dimensional Rayleigh
    gas with semipermeable barriers. Communications in Mathematical Physics. 143(3),
    451–466.
  mla: Erdös, László, and Dao Tuyen. “Central Limit Theorems for the One-Dimensional
    Rayleigh Gas with Semipermeable Barriers.” <i>Communications in Mathematical Physics</i>,
    vol. 143, no. 3, Springer, 1992, pp. 451–66, doi:<a href="https://doi.org/10.1007/BF02099260">10.1007/BF02099260</a>.
  short: L. Erdös, D. Tuyen, Communications in Mathematical Physics 143 (1992) 451–466.
date_created: 2018-12-11T11:59:15Z
date_published: 1992-01-01T00:00:00Z
date_updated: 2022-03-16T14:24:12Z
day: '01'
doi: 10.1007/BF02099260
extern: '1'
intvolume: '       143'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-143/issue-3/Central-limit-theorems-for-the-one-dimensional-Rayleigh-gas-with/cmp/1104249076.full
month: '01'
oa: 1
oa_version: Published Version
page: 451 - 466
publication: Communications in Mathematical Physics
publication_identifier:
  issn:
  - 0010-3616
publication_status: published
publisher: Springer
publist_id: '4170'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Central limit theorems for the one-dimensional Rayleigh gas with semipermeable
  barriers
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 143
year: '1992'
...