Advances in discrete dynamics / edited by Jose S. Canovas.

Contributor(s):

Cánovas, José S

Material type: Text

TextSeries: Mathematics research developments seriesPublisher: Hauppauge, New York : Nova Science Publishers, [2012]Description: 1 online resourceContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9781624173370
1624173373

Subject(s):

Genre/Form:

Additional physical formats: Print version:: Advances in discrete dynamicsDDC classification:

003/.83 22

LOC classification:

QA845

Online resources:

Click here to access online

Contents:

SHADOWING TECHNIQUES AND CHAOTIC PHENOMENAAbstract; 1. Introduction; 2. POTPandChaos; 3. TheLmSPandRecurrence; 3.1. AsymptoticPseudoOrbitandChainRecurrentSet; 3.2. LmSPandItsBasicProperty; 3.3. LmSPandInverseLimitSpace; 3.4. LmSP, MixingandRecurrency; 4. AverageShadowingProperty; 4.1. ASPandChainRecurrenceProperty; 4.2. ASPandTopologicalTransitivity; 5. AsymptoticAverageShadowingProperty; 5.1. AASPandChainTransitivity; 5.2. AASPandTopologicalTransitivity; 5.3. MapswiththeAASP; 6. Conclusion; Acknowledgement; References;!-LIMIT SETS OF DISCRETE-TIME DYNAMICAL SYSTEMS; Abstract.

1. Discrete-Time(Autonomous)DynamicalSystems1.1.!-limitSets, Periodicity, Recurrence, andNon-wonderingPoints; 1.2.!-limitSetsontheUnitInterval; 1.3. MinimalSets; 2. Chaos; 2.1. ThreeFormsofChaos; 3. GenericnessinTopologicalDynamics:TypicalBehaviour; 3.1. UbiquityofAddingMachinesinTopologicalDynamicalSystems; 4. Non-autonomousDynamicalSystemsontheUnitInterval; 4.1. AlternatingSystems, andTheir!-limitSets; 5. Conclusion; 5.1. Concerning!-limitSets; 5.2. ConcerningChaos; References; TOPOLOGICAL ENTROPY IN ONE DIMENSIONAL DYNAMICS; Abstract; 1. Introduction:Entropy.

2. TopologicalEntropy:FirstDefinitionsandBasicProperties3. TopologicalEntropy, TopologicalDynamicsandTopologicalChaos; 4. ContinuousIntervalMaps; 4.1. PiecewiseMonotoneMaps; 4.2. Horseshoes; 4.3.ComputingTopologicalEntropy:AFirstApproach; 4.4. ContinuityPropertiesofTopologicalEntropy; 4.5. TopologicalEntropyandTransitivity; 4.6. TopologicalEntropyandChaosforContinuousIntervalMaps; 4.7.ComputingTopologicalEntropyofUnimodalMaps; 4.8. TopologicalEntropyandPermutations; 4.9. MiscellaneousResults; 5. ContinuousRealMaps; 5.1. DefinitionofTopologicalEntropyonnonCompactSpaces.

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