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Jezierski J., Marzantowicz W. — Homotopy Methods in Topological Fixed and Periodic Points Theory
Jezierski J., Marzantowicz W. — Homotopy Methods in Topological Fixed and Periodic Points Theory

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Название: Homotopy Methods in Topological Fixed and Periodic Points Theory

Авторы: Jezierski J., Marzantowicz W.

Аннотация:

This is the first systematic and self-contained textbook on homotopy methods in the study of periodic points of a map. A modern exposition of the classical topological fixed-point theory with a complete set of all the necessary notions as well as new proofs of the Lefschetz-Hopf and Wecken theorems are included.

Periodic points are studied through the use of Lefschetz numbers of iterations of a map and Nielsen-Jiang periodic numbers related to the Nielsen numbers of iterations of this map. Wecken theorem for periodic points is then discussed in the second half of the book and several results on the homotopy minimal periods are given as applications, e.g. a homotopy version of the Åarkovsky theorem, a dynamics of equivariant maps, and a relation to the topological entropy. Students and researchers in fixed point theory, dynamical systems, and algebraic topology will find this text invaluable.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2006

Количество страниц: 319

Добавлена в каталог: 27.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Action, free      283
Action, the second Reidemeister      183
Algebra, Heisenberg      272
Algebra, Lie      243
Alseda      240
Andres      294
Approximation, homotopy      45
Approximation, smooth      13
Arnold      106
Babienko      63 69 95 107
Baldwin      240
Begle      295
Block      240
Bogatyi      63 69 95 107
Bonino      291 292
Bottle, Klein      243 279
Bowszyc      69 70
Brooks      161
Brouwer      5
Browder      4
Brown M.      291
Brown R.      161 165
Character of integral representation      79
Character, finite-dimensional      80
Characteristic of field      43
Characteristic, Euler of graded endomorphism      69
Chow      84 90
Class, essential      120
Class, H-Nielsen, essential      137
Class, inessential      120
Class, Nielsen      120
Class, Reidemeister      125
Classes, H-Reidemeister      137
Classes, Nielsen      120 156
Classes, Reidemeister      124 156
Cohomology      42
Complex, Chevalley — Eilenberg      255
Complex, CW, finite      41
Complex, de Rham      255
Condition, Cauchy initial      3
Congruences, Dold      57 63 81
Conjecture, Arnold      106
Conjecture, Poincare      139
Conjecture, Shub — Sullivan      94
Contractible, locally      120
Contraction      3
Cronin      105
CW-complex      32
Davey      279
Degree of map      12
Degree, homologic definition      20
Degree, properties of      21
Degree, uniqueness of      26
Density, natural      115
Density, natural density of set      78
Depth of a Reidemeister class      193
Determinant, Vandermonde      67
Diagonal      5
Dold      60
Duality, Poincare      184
Duan      111
Dugundji      53
Efremova      240
Eigenvalue, essential      68
Eigenvalue, quotient      112
Eilenberg      295
Element, decomposable in cohomology      111
Example, Shub      55 238
Expansion, k-periodic      79 81
Expansion, k-periodic, coefficient      81
Fadell      139 177 248
Fagella      107
Ferrario      285
Fibration, Hopf      166
Fibration, Hurewicz      166 181
Field      38
Field number      39
Field of coefficients      43
Formula, Hopf index      100
Formula, Lefschetz — Hopf      11
Formula, Lefschetz — Hopf index      49
Formula, Moebius inversion      57 264
Formula, summation      257
Franks      90 103 293
Fuller      70
Function, arithmetic      57
Function, boosting      192
Function, generating      63
Function, Moebius      57
Function, Uryshon      218
Goehde      4
Gorniewicz      294
Graff      113
Granas      53
Group, completely solvable      244
Group, exponential      245
Group, fundamental      7
Group, Galois      66
Group, Lie      49
Group, n-homology      19
Group, nilpotent      241
Group, solvable      241
Group, unimodular      275
Guckenheimer      240
Guckenheimer, Duan      116
Halpern      189 279
Hart      279
Hattori      255
Heath      197
Homeomorphism, le Calvez — Yoccoz      293
Homeomorphism, minimal      293
Homology      42
Homology, Cech      295
Homology, spaces      43
Homotopy      5
Homotopy, equivariant      284
Hopf      119
Husseini      139 177 248
Index of periodicity of graded matrix      68
Index of periodicity of map      69
Index, Conley      293
Index, fixed point      29
Index, fixed point, additivity property      30
Index, fixed point, commutativity property      31
Index, fixed point, for ENRs maps      32
Index, fixed point, homotopy invariance property      31
Index, fixed point, localization property      30
Index, fixed point, multiplicativity property      31
Index, fixed point, properties      30
Index, fixed point, units property      30
Index, Fuller      69
Index, periodic      83
Integers, gaussian      242
Isomorphism, Hurewicz      25
Jezierski      208 225 280
Jiang      7 113 138 150 156 189 196
Katok A.      286
Katok S.      290
Kelly      139
Keppelmann      189 197 245
Kiang      7
Kirk      4
Komendarczyk      267
Kronecker on density of multiplies of irrational angle      75 76
Kronecker on roots of monic polynomial      72 262
Kronecker — Weyl      79
Krzyzewski      290
Lattice      242
le Calvez      293
Lefschetz      6 119
Lefschetz fixed point      52
Lefschetz — Hopf      49
Lefschetz — Hopf, fixed point      11
Lefschetz — Hopf, periodic point      55
Lemma, Fatou for polynomials      65
Lemma, generalized homotopy invariance      28
Lemma, Hopf      220
Lemma, Hopf for degree      24
Lemma, Hopf for fixed point index      37
Lemma, Hopf for trace      45
Lemma, Whitney      139
Length of nilpotency      246
Llibre      107 113 240 279
Malcev      246 248
Mallet-Paret      84 90
Manifold, topological      32
Manifolds, Heisenberg      242
Manifolds, Iwasawa      242
Map, cellular      47 49
Map, characteristic      50
Map, compactly fixed      29
Map, completely continuous      9
Map, d-compact      12
Map, equivariant      283
Map, essentially reducible      198
Map, essentially reducible to GCD      198
Map, essentially toral      200
Map, holomorphic      104
Map, homotopic      5
Map, Lipschitz      4
Map, multivalued      294
Map, multivalued, admisible      295
Map, multivalued, given by a pair      294
Map, multivalued, upper semicontinuous      294
Map, non-expansive      4
Map, proximity      145
Map, simplical      47
Map, transversal      99
Map, Vietoris      295
Marzantowicz      84 90
Matrix, unimodular      247
Matrix, Vandermonde      77
Matsuoka      90 102
McCord      245 248
Measure, Lebesgue      13
Misiurewicz      240 285
Module, free      38
Module, projective      47
Montgomery      295
Mostow      242
Newton on symmetric polynomials      58
Nielsen      7 119 123 138
Nilmanifold      241
Number of Reidemeister classes      156
Number, H-Nielsen      137
Number, Lefschetz      2 6 42
Number, Lefschetz, universal      46
Number, Nielsen      120
Number, Nielsen — Jiang periodic, full      196
Number, Nielsen — Jiang periodic, prime      196
Number, Nielsen, asymptotic      287
Numbers, Lehmer — Lucas      266
Orbits of Reidemeister classes      195
Orientation along a compact subset      20
Orientation of Euclidean space      19
Orientation, homological      19
Pak      161
Period, homotopy minimal      239
Period, minimal      2
Periods, homotopy minimal, algebraic      259
Point, critical      12
Point, fixed      1
Point, inverting      100
Point, noninverting      100
Point, periodic      1
Point, regular      12
Point, twisted      100
Point, untwisted      100
Polynomial, characteristic      39
Polynomial, cohomology characteristic      112
Polynomial, cyclotomic      73 103
Polynomial, monic      41
Polynomial, Newton      58
Polynomial, symmetric      58
Principle, Banach Contraction      3
Problem, Ulam      293
Procedure, cancelling      209
Property, Darboux      6
Przygodzki      84 90
Przytycki      285 290
Radius, spectral, essential      68
Rank of rational exterior power      112
Reidemeister      119
Relation, Nielsen      120
Relation, Reidemeister      177
Representation, adjoint      244
Representation, regular      81
Resolution, projective      47
Rigidity of lattices      244
Ring number      39
Ring, commutative      38
Ring, principal ideals      47
Ruelle      290
Ruiz de Portal      293
Salazar      293
Sard      11 12
Sarkovskii      240
Sarkovskii type      279
Schauder      9
Schinzel      240 265
Schmitt      291
Sequence, Mayer Vietoris exact      61
Set of all roots of unity      103
Set of fixed points      1
Set of homotopy minimal periods      239
Set of minimal periods      2
Set of periodic points      1
Shi      138 145 150
Shub      7 84 94 285
Shub — Sullivan      84 91
Siegberg      85
simplex      19
Solvmanifold      241
Solvmanifold, completely solvable      244
Solvmanifold, exponential      245
Solvmanifold, N R-solvmanifold      245 253
Space, Banach      3
Space, contractible      52
Space, essentially reducible      198
Space, essentially reducible to GCD      198
Space, Jiang      157
Space, normed linear      9
Space, projective      279
Space, rational exterior      112
Space, rational exterior, simple      112
Space, rational Hopf, simple      116
Space, weakly Jiang      159
Sullivan      84 94
Swanson      240
Szlenk      240
Taylor      161
Theorem, Anosov      245
Theorem, Auslander      243
Theorem, Brouwer      6 53
Theorem, Cartan      273
Theorem, Chow, Mallet — Paret and Yorke      84
Theorem, Cronin      105
Theorem, Dirichlet on arithmetic progression      74
Theorem, Dold      60
Theorem, Fermat little      57
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