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Resumenes 146 • Si X es compacto entonces : f periódicamente densa⇒ f periódicamente densa • f es mezclante ⇔ f es mezclante • f tieneentropía topológica positiva ⇔ f tieneentropía topológica positiva También, diversos aspectos teóricos y aplicados en abierto serán discutidos. Individual and collective dynamics: chaotic relations 2 It is well known that a numerous class of real problems are modelled by a discrete dynamical system xn + 1 = f ( xn ), n = 0, 1, 2,... (1) where ( X , d) is a metric space and f : X → X is a continuous function. The basic goal of the theory of discrete dynamical systems (DDS) is to 2 n understand the nature of all orbits x, f ( x), f ( x), ...., f ( x) as n becomes large and, generally, this is an impossible task. In certain sense, the study of the orbits in a DDS says us as are moved the points in the base space X and, in many cases, these orbits presents a chaotic structure. On the other hand, sometimes is not sufficient to know as are moved the points in the base space X but it is necessary to know as are moved the subsets of X what carries us to the problem of analyzing the dynamics of set-valued dynamical discrete systems (SDDS). For example, it is usual today to put special transmitters on different types of biological species to know their movements within their habitats. Thus, if we denote by X the habitat of a given specie and we choose an individual representative x ∈ X , then we can obtain information about the movement of x in the ecosystem X and, of this way, we can construct an individual displacement function f : X → X . Eventually, this function could be chaotic or not, but the question now it is the following: What is the connection between the dynamic of individual movement and the dynamic of collective movement? In this direction, given a dynamical discrete system (1) we consider the setvalued dynamical discrete system (SDDS) associated to f : An + 1 = f ( An ), n = 0, 1, 2,... (2) where f : K( X ) → K( X ) , f ( A) = f ( A) = { f ( a) / a ∈ A} , is the natural extension of f to K (X ) . In this context, our main goal in this work is studying the following fundamental question: individual chaos implies collective chaos? and conversely? As a partial response to this question above, if we consider the space ( K ( X ), H ) of all nonempty compacts subsets of X endowed with the Hausdorff metric induced by d , then the following chaotic relationships between f and f are showed: • f transitive ⇒ f transitive • f sensitively dependent ⇒ f sensitively dependent • If X is compact then : f periodically dense ⇒ f periodically dense 2 Trabajo financiado por Conicyt-Chile vía Proyecto 1040303 y Dipog-UTA vía Proyecto 4731-04.
Resumenes 147 • f mixing ⇔ f mixing • Thetopological entropy of f is positive⇔ the topological entropy of f is positive Also, several open theoretical and applied topics will be discussed. Referencias [1] J. Banks, Chaos for induced hyperspace maps, Chaos, Solitons & Fractals 25 (2005), 681-685. [2] J.Cánovas and G. Soler, Topological entropy for induced hyperspace maps, pre-print. [3] A. Fedeli, On chaotic set-valued discrete dynamical systems, Chaos, Solitons & Fractals 23 (2005), 1381-1384. [4] A. Peris, Set-valued discrete chaos, Chaos, Solitons & Fractals 26 (2005), 19-23. [5] H. Román-Flores, A note on transitivity in set-valued discrete systems, Chaos, Solitons & Fractals 17 (2003), 99-104. [6] H.Román-Flores and Y. Chalco-Cano, Robinson´s chaos in set-valued discrete systems, Chaos, Solitons & Fractals 25 (2005), 33-42.
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ORGANIZADO POR LA SOCIEDAD LATINOAM
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(en orden alfabético) COMITÉ CIEN
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CURSILLOS Cursillo Nº1: Dinámica
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CONFERENCIAS INVITADAS
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Conferencias 10 Estabilidad y persi
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Conferencias 12 (K, the ‘carrying
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Conferencias 14 Víctimas Inmigrant
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Conferencias 16 Influencia de la di
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Resumenes 19 Bifurcaciones de Hopf
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Resumenes 21 where y = y(t) represe
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Resumenes 23 Dinámica del modelo d
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Resumenes 25 In this work, we propo
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Resumenes 27 Simulação computacio
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Resumenes 29 of the minisymposium:
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Resumenes 31 Honeybee, Apis mellife
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Resumenes 33 The minimum ratio is t
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Resumenes 35 [1] On the role of end
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Resumenes 37 Modelo matemático de
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Resumenes 39 Figure 1: Plano de fas
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Resumenes 41 Dinámica de poblacion
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Resumenes 43 El método de las solu
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Resumenes 45 Dinámica de un tumor
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Resumenes 47 Several cancer models
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Resumenes 49 process is physically
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Resumenes 51 For the analysis of fr
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Resumenes 53 Sustainability in floo
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Resumenes 55 Sincronismo em redes d
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Resumenes 57 Um modelo de autômato
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Resumenes 59 Um modelo matemático
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Resumenes 61 Redes de mapas acoplad
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Resumenes 63 Sobre la dinámica de
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Resumenes 65 Un modelo de depredaci
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Resumenes 67 There exists wide evid
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Resumenes 69 Modelado del control n
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Resumenes 71 Modelo de red neuronal
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Resumenes 73 Efectos de la radiaci
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Resumenes 75 Un modelo matemático
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Resumenes 77 Estudio comparativo de
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Resumenes 79 Introduction The proje
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Resumenes 81 formulation to obtain
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Resumenes 83 tiene un único punto
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Resumenes 85 [4] Courchamp, F., Clu
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Resumenes 87 An important part of a
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Resumenes 89 A(H3N2). Starting in V
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Resumenes 91 i) Panmixia, donde se
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Resumenes 93 punto de equilibrio y
Page 97 and 98: Resumenes 95 Un modelo epidemiológ
Page 99 and 100: Resumenes 97 Aproximación saddlepo
Page 101 and 102: Resumenes 99 [3] Daniels, H. E. 196
Page 103 and 104: Resumenes 101 bloqueados. El nudo q
Page 105 and 106: Resumenes 103 Referencias • Stauf
Page 107 and 108: Resumenes 105 Un modelo dinámico d
Page 109 and 110: Resumenes 107 Un modelo en ecuacion
Page 111 and 112: Resumenes 109 The mite show a prefe
Page 113 and 114: Resumenes 111 Ondas viajantes en un
Page 115 and 116: Resumenes 113 [5] Pregnolatto S. de
Page 117 and 118: Resumenes 115 All this will enable
Page 119 and 120: Resumenes 117 Extensión de un mode
Page 121 and 122: Resumenes 119 ∂C ∂C C = 0. = 0.
Page 123 and 124: Resumenes 121 Comparación de Enfoq
Page 125 and 126: Resumenes 123 Refúgios Espaciais e
Page 127 and 128: Resumenes 125 La dinámica del sest
Page 129 and 130: Resumenes 127 Dinámica poblacional
Page 131 and 132: Resumenes 129 Aproximación y simul
Page 133 and 134: Resumenes 131 An age-structured fin
Page 135 and 136: Resumenes 133 Respuestas demográfi
Page 137 and 138: Resumenes 135 Modelando el efecto A
Page 139 and 140: Resumenes 137 the Allee effect are
Page 141 and 142: Resumenes 139 Tratamientos de endom
Page 143 and 144: Resumenes 141 Implicaciones del efe
Page 145 and 146: Resumenes 143 phenomenon has been e
Page 147: Resumenes 145 Dinámica individual
Page 151 and 152: Resumenes 149 Introduction The inve
Page 153 and 154: Resumenes 151 DNA microarrays are t
Page 155 and 156: Resumenes 153 V. Cholerae: Primeros
Page 157 and 158: Resumenes 155 Análisis cuantitativ
Page 159 and 160: Resumenes 157 Dinámica de un model
Page 161 and 162: Resumenes 159 Obtención de paráme
Page 163 and 164: Resumenes 161 [4] Nagy K. A (1987)
Page 165 and 166: Resumenes 163 diferencial automáti
Page 167 and 168: Resumenes 165 The localized peaks S
Page 169 and 170: Resumenes 167 obteniéndose que sie
Page 171 and 172: Resumenes 169 [CLARK 90] Clark, C.
Page 173 and 174: Resumenes 171 Numerical algorithms
Page 175 and 176: Resumenes 173 The second method of
Page 177 and 178: Resumenes 175 los parámetros son t
Page 179 and 180: Resumenes 177 Bifurcación hacia at
Page 181 and 182: Resumenes 179 Malaria is the tropic
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