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  1. Journal of Dynamics and Differential Equations
  2. Journal of Dynamics and Differential Equations : Volume 23
  3. Journal of Dynamics and Differential Equations : Volume 23, Issue 1, March 2011
  4. Local Fixed Point Indices of Iterations of Planar Maps
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Journal of Dynamics and Differential Equations : Volume 29
Journal of Dynamics and Differential Equations : Volume 28
Journal of Dynamics and Differential Equations : Volume 27
Journal of Dynamics and Differential Equations : Volume 26
Journal of Dynamics and Differential Equations : Volume 25
Journal of Dynamics and Differential Equations : Volume 24
Journal of Dynamics and Differential Equations : Volume 23
Journal of Dynamics and Differential Equations : Volume 23, Issue 4, December 2011
Journal of Dynamics and Differential Equations : Volume 23, Issue 3, September 2011
Journal of Dynamics and Differential Equations : Volume 23, Issue 2, June 2011
Journal of Dynamics and Differential Equations : Volume 23, Issue 1, March 2011
Existence, Uniqueness, and Stability of Generalized Traveling Waves in Time Dependent Monostable Equations
Symmetry of Positive Solutions of Asymptotically Symmetric Parabolic Problems on $${{\mathbb R}^N}$$
Continuation of the Periodic Orbits for the Differential Equation with Discontinuous Right Hand Side
Isolas of 2-Pulse Solutions in Homoclinic Snaking Scenarios
Well Adapted Normal Linearization in Singular Perturbation Problems
Periodic Solutions and Invariant Manifolds for an Even-Order Differential Equation with Power Nonlinearity
Traveling Monotonic Fronts in the Discrete Nagumo Equation
Dynamics of Quasiconformal Fields
Local Fixed Point Indices of Iterations of Planar Maps
Journal of Dynamics and Differential Equations : Volume 22
Journal of Dynamics and Differential Equations : Volume 21
Journal of Dynamics and Differential Equations : Volume 20
Journal of Dynamics and Differential Equations : Volume 19
Journal of Dynamics and Differential Equations : Volume 18
Journal of Dynamics and Differential Equations : Volume 17
Journal of Dynamics and Differential Equations : Volume 16
Journal of Dynamics and Differential Equations : Volume 15
Journal of Dynamics and Differential Equations : Volume 14
Journal of Dynamics and Differential Equations : Volume 13
Journal of Dynamics and Differential Equations : Volume 12
Journal of Dynamics and Differential Equations : Volume 11
Journal of Dynamics and Differential Equations : Volume 10
Journal of Dynamics and Differential Equations : Volume 9

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Local Fixed Point Indices of Iterations of Planar Maps

Content Provider Springer Nature Link
Author Graff, Grzegorz Ruiz del Portal, Francisco R. wak Przygodzki, Piotr
Copyright Year 2011
Abstract Let $${f: U\rightarrow {\mathbb R}^2}$$ be a continuous map, where U is an open subset of $${{\mathbb R}^2}$$ . We consider a fixed point p of f which is neither a sink nor a source and such that {p} is an isolated invariant set. Under these assumption we prove, using Conley index methods and Nielsen theory, that the sequence of fixed point indices of iterations $${\{{\rm ind}(f^n,p)\}_{n=1}^\infty}$$ is periodic, bounded from above by 1, and has infinitely many non-positive terms, which is a generalization of Le Calvez and Yoccoz theorem (Annals of Math., 146, 241–293 (1997)) onto the class of non-injective maps. We apply our result to study the dynamics of continuous maps on 2-dimensional sphere.
Ending Page 223
Page Count 11
Starting Page 213
File Format PDF
ISSN 10407294
e-ISSN 15729222
Journal Journal of Dynamics and Differential Equations
Issue Number 1
Volume Number 23
Language English
Publisher Springer US
Publisher Date 2011-01-21
Publisher Place Boston
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Fixed point index Periodic points Ordinary Differential Equations Conley index Homeomorphisms and diffeomorphisms of planes and surfaces Fixed points, periodic points, fixed-point index theory Index theory, Morse-Conley indices Applications of Mathematics Iterations Nielsen number Partial Differential Equations
Content Type Text
Resource Type Article
Subject Analysis
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