March  2008, 7(2): 457-463. doi: 10.3934/cpaa.2008.7.457

Discrete-time theorems for the dichotomy of one-parameter semigroups

1. 

Department of Mathematics, University of California, Los Angeles, CA 90095, United States

Received  February 2007 Revised  July 2007 Published  December 2007

Discrete-time sufficient conditions for the dichotomy of $C_0$-semigroups are obtained in the general case when it is not required that the kernel of the dichotomic projector to be $T(t)$-invariant. Thus are extended known results due to Datko, Pazy, Zabczyk.
Citation: Ciprian Preda. Discrete-time theorems for the dichotomy of one-parameter semigroups. Communications on Pure & Applied Analysis, 2008, 7 (2) : 457-463. doi: 10.3934/cpaa.2008.7.457
[1]

Manuela Giampieri, Stefano Isola. A one-parameter family of analytic Markov maps with an intermittency transition. Discrete & Continuous Dynamical Systems - A, 2005, 12 (1) : 115-136. doi: 10.3934/dcds.2005.12.115

[2]

Daniel Schnellmann. Typical points for one-parameter families of piecewise expanding maps of the interval. Discrete & Continuous Dynamical Systems - A, 2011, 31 (3) : 877-911. doi: 10.3934/dcds.2011.31.877

[3]

Stephen C. Preston, Alejandro Sarria. One-parameter solutions of the Euler-Arnold equation on the contactomorphism group. Discrete & Continuous Dynamical Systems - A, 2015, 35 (5) : 2123-2130. doi: 10.3934/dcds.2015.35.2123

[4]

Jun Hu, Oleg Muzician, Yingqing Xiao. Dynamics of regularly ramified rational maps: Ⅰ. Julia sets of maps in one-parameter families. Discrete & Continuous Dynamical Systems - A, 2018, 38 (7) : 3189-3221. doi: 10.3934/dcds.2018139

[5]

Gabriele Link. Hopf-Tsuji-Sullivan dichotomy for quotients of Hadamard spaces with a rank one isometry. Discrete & Continuous Dynamical Systems - A, 2018, 38 (11) : 5577-5613. doi: 10.3934/dcds.2018245

[6]

João Marcos do Ó, Abbas Moameni. Solutions for singular quasilinear Schrödinger equations with one parameter. Communications on Pure & Applied Analysis, 2010, 9 (4) : 1011-1023. doi: 10.3934/cpaa.2010.9.1011

[7]

Xiaoyu Zheng, Peter Palffy-Muhoray. One order parameter tensor mean field theory for biaxial liquid crystals. Discrete & Continuous Dynamical Systems - B, 2011, 15 (2) : 475-490. doi: 10.3934/dcdsb.2011.15.475

[8]

Viorel Nitica, Andrei Török. On a semigroup problem. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 2365-2377. doi: 10.3934/dcdss.2019148

[9]

Christian Pötzsche. Dichotomy spectra of triangular equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (1) : 423-450. doi: 10.3934/dcds.2016.36.423

[10]

J. W. Neuberger. How to distinguish a local semigroup from a global semigroup. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5293-5303. doi: 10.3934/dcds.2013.33.5293

[11]

Andrzej Biś. Entropies of a semigroup of maps. Discrete & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 639-648. doi: 10.3934/dcds.2004.11.639

[12]

Carlos Cabrera, Peter Makienko, Peter Plaumann. Semigroup representations in holomorphic dynamics. Discrete & Continuous Dynamical Systems - A, 2013, 33 (4) : 1333-1349. doi: 10.3934/dcds.2013.33.1333

[13]

António J.G. Bento, Nicolae Lupa, Mihail Megan, César M. Silva. Integral conditions for nonuniform $μ$-dichotomy on the half-line. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3063-3077. doi: 10.3934/dcdsb.2017163

[14]

Kristin Dettmers, Robert Giza, Rafael Morales, John A. Rock, Christina Knox. A survey of complex dimensions, measurability, and the lattice/nonlattice dichotomy. Discrete & Continuous Dynamical Systems - S, 2017, 10 (2) : 213-240. doi: 10.3934/dcdss.2017011

[15]

Thorsten Hüls. Numerical computation of dichotomy rates and projectors in discrete time. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 109-131. doi: 10.3934/dcdsb.2009.12.109

[16]

Mihail Megan, Adina Luminiţa Sasu, Bogdan Sasu. Discrete admissibility and exponential dichotomy for evolution families. Discrete & Continuous Dynamical Systems - A, 2003, 9 (2) : 383-397. doi: 10.3934/dcds.2003.9.383

[17]

Nguyen Thieu Huy, Ngo Quy Dang. Dichotomy and periodic solutions to partial functional differential equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3127-3144. doi: 10.3934/dcdsb.2017167

[18]

Jana Kopfová. Nonlinear semigroup methods in problems with hysteresis. Conference Publications, 2007, 2007 (Special) : 580-589. doi: 10.3934/proc.2007.2007.580

[19]

Renato Iturriaga, Héctor Sánchez Morgado. The Lax-Oleinik semigroup on graphs. Networks & Heterogeneous Media, 2017, 12 (4) : 643-662. doi: 10.3934/nhm.2017026

[20]

Bin Chen, Xiongping Dai. On uniformly recurrent motions of topological semigroup actions. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 2931-2944. doi: 10.3934/dcds.2016.36.2931

2017 Impact Factor: 0.884

Metrics

  • PDF downloads (5)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]