American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Existence and monotonicity property of minimizers of a nonconvex variational problem with a second-order Lagrangian
  • DCDS Home
  • This Issue
  • Next Article
    Structural stability of solutions to the Riemann problem for a scalar nonconvex CJ combustion model
July  2009, 25(2): 669-685. doi: 10.3934/dcds.2009.25.669

Hölder forms and integrability of invariant distributions

Slobodan N. Simić 1,

1. 

Department of Mathematics, San José State University, San José, CA 95192-0103, United States

Received  June 2008 Revised  January 2009 Published  June 2009

We prove an inequality for Hölder continuous differential forms on compact manifolds in which the integral of the form over the boundary of a sufficiently small, smoothly immersed disk is bounded by a certain multiplicative convex combination of the volume of the disk and the area of its boundary. This inequality has natural applications in dynamical systems, where Hölder continuity is ubiquitous. We give two such applications. In the first one, we prove a criterion for the existence of global cross sections to Anosov flows in terms of their expansion-contraction rates. The second application provides an analogous criterion for non-accessibility of partially hyperbolic diffeomorphisms.
Keywords: global cross section, invariant distribution, Hölder forms.
Mathematics Subject Classification: Primary: 37D20, 37D30; Secondary: 49Q1.
Citation: Slobodan N. Simić. Hölder forms and integrability of invariant distributions. Discrete & Continuous Dynamical Systems, 2009, 25 (2) : 669-685. doi: 10.3934/dcds.2009.25.669
[1]

Charles Pugh, Michael Shub, Amie Wilkinson. Hölder foliations, revisited. Journal of Modern Dynamics, 2012, 6 (1) : 79-120. doi: 10.3934/jmd.2012.6.79
[2]

Jinpeng An. Hölder stability of diffeomorphisms. Discrete & Continuous Dynamical Systems, 2009, 24 (2) : 315-329. doi: 10.3934/dcds.2009.24.315
[3]

Gang Bao, Jun Lai. Radar cross section reduction of a cavity in the ground plane: TE polarization. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 419-434. doi: 10.3934/dcdss.2015.8.419
[4]

Luis Barreira, Claudia Valls. Hölder Grobman-Hartman linearization. Discrete & Continuous Dynamical Systems, 2007, 18 (1) : 187-197. doi: 10.3934/dcds.2007.18.187
[5]

Rafael De La Llave, R. Obaya. Regularity of the composition operator in spaces of Hölder functions. Discrete & Continuous Dynamical Systems, 1999, 5 (1) : 157-184. doi: 10.3934/dcds.1999.5.157
[6]

Luca Lorenzi. Optimal Hölder regularity for nonautonomous Kolmogorov equations. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 169-191. doi: 10.3934/dcdss.2011.4.169
[7]

Vincent Lynch. Decay of correlations for non-Hölder observables. Discrete & Continuous Dynamical Systems, 2006, 16 (1) : 19-46. doi: 10.3934/dcds.2006.16.19
[8]

Andrey Kochergin. A Besicovitch cylindrical transformation with Hölder function. Electronic Research Announcements, 2015, 22: 87-91. doi: 10.3934/era.2015.22.87
[9]

Walter Allegretto, Yanping Lin, Shuqing Ma. Hölder continuous solutions of an obstacle thermistor problem. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 983-997. doi: 10.3934/dcdsb.2004.4.983
[10]

Pedro Duarte, Silvius Klein, Manuel Santos. A random cocycle with non Hölder Lyapunov exponent. Discrete & Continuous Dynamical Systems, 2019, 39 (8) : 4841-4861. doi: 10.3934/dcds.2019197
[11]

Arturo Echeverría-Enríquez, Alberto Ibort, Miguel C. Muñoz-Lecanda, Narciso Román-Roy. Invariant forms and automorphisms of locally homogeneous multisymplectic manifolds. Journal of Geometric Mechanics, 2012, 4 (4) : 397-419. doi: 10.3934/jgm.2012.4.397
[12]

Patrick Foulon, Boris Hasselblatt. Lipschitz continuous invariant forms for algebraic Anosov systems. Journal of Modern Dynamics, 2010, 4 (3) : 571-584. doi: 10.3934/jmd.2010.4.571
[13]

Ahmed El Kaimbillah, Oussama Bourihane, Bouazza Braikat, Mohammad Jamal, Foudil Mohri, Noureddine Damil. Efficient high-order implicit solvers for the dynamic of thin-walled beams with open cross section under external arbitrary loadings. Discrete & Continuous Dynamical Systems - S, 2019, 12 (6) : 1685-1708. doi: 10.3934/dcdss.2019113
[14]

Samia Challal, Abdeslem Lyaghfouri. Hölder continuity of solutions to the $A$-Laplace equation involving measures. Communications on Pure & Applied Analysis, 2009, 8 (5) : 1577-1583. doi: 10.3934/cpaa.2009.8.1577
[15]

Lili Li, Chunrong Chen. Nonlinear scalarization with applications to Hölder continuity of approximate solutions. Numerical Algebra, Control & Optimization, 2014, 4 (4) : 295-307. doi: 10.3934/naco.2014.4.295
[16]

Eugen Mihailescu. Unstable manifolds and Hölder structures associated with noninvertible maps. Discrete & Continuous Dynamical Systems, 2006, 14 (3) : 419-446. doi: 10.3934/dcds.2006.14.419
[17]

Alexander I. Bufetov. Hölder cocycles and ergodic integrals for translation flows on flat surfaces. Electronic Research Announcements, 2010, 17: 34-42. doi: 10.3934/era.2010.17.34
[18]

Łukasz Struski, Jacek Tabor. Expansivity implies existence of Hölder continuous Lyapunov function. Discrete & Continuous Dynamical Systems - B, 2017, 22 (9) : 3575-3589. doi: 10.3934/dcdsb.2017180
[19]

Eugen Mihailescu. Approximations for Gibbs states of arbitrary Hölder potentials on hyperbolic folded sets. Discrete & Continuous Dynamical Systems, 2012, 32 (3) : 961-975. doi: 10.3934/dcds.2012.32.961
[20]

Lucio Boccardo, Alessio Porretta. Uniqueness for elliptic problems with Hölder--type dependence on the solution. Communications on Pure & Applied Analysis, 2013, 12 (4) : 1569-1585. doi: 10.3934/cpaa.2013.12.1569

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (41)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences