Mixing
Possibilites for Sharkovskii's theorem. [closed]
Clash Royale CLAN TAG#URR8PPP
up vote
-2
down vote
favorite
Hello I am interested in Sharkovskii's theorem with respect to two aspects:
- Possibilities of generalization for other spaces with some additional structures or dimensions.
- Applications in dynamical systems, other branches of mathematics and real life(!?)
Some references are appreciated.
dynamical-systems
edited Jul 21 at 1:55
David_Shmij
398116
asked Jul 21 at 0:49
C. Junior
637311
closed as too broad by Did, Taroccoesbrocco, max_zorn, Jose Arnaldo Bebita Dris, Parcly Taxel Jul 22 at 13:33
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |Â
up vote
-2
down vote
favorite
Hello I am interested in Sharkovskii's theorem with respect to two aspects:
- Possibilities of generalization for other spaces with some additional structures or dimensions.
- Applications in dynamical systems, other branches of mathematics and real life(!?)
Some references are appreciated.
dynamical-systems
edited Jul 21 at 1:55
David_Shmij
398116
asked Jul 21 at 0:49
C. Junior
637311
closed as too broad by Did, Taroccoesbrocco, max_zorn, Jose Arnaldo Bebita Dris, Parcly Taxel Jul 22 at 13:33
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
Could you please be a bit more specific as to what generalizations you are looking for? As to the applications, Sharkovskii's theorem is a result on periodicity of dynamical systems.
– David_Shmij
Jul 21 at 1:49
1
I would recommend you read the paper "Period Three Implies Chaos" by Tien-Yien Li & James A. Yorke
– David_Shmij
Jul 21 at 2:02
Just try Googling Sharkovskii theorem.
– user539887
Jul 21 at 8:59
4
Almost the same question was posted in MO References and background on Sharkovskii's theorem. I think that simultaneous cross-posting, without mentioning it, is considered a bad practice
– user539887
Jul 21 at 9:49
add a comment |Â
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
Hello I am interested in Sharkovskii's theorem with respect to two aspects:
- Possibilities of generalization for other spaces with some additional structures or dimensions.
- Applications in dynamical systems, other branches of mathematics and real life(!?)
Some references are appreciated.
dynamical-systems
edited Jul 21 at 1:55
David_Shmij
398116
asked Jul 21 at 0:49
C. Junior
637311
Hello I am interested in Sharkovskii's theorem with respect to two aspects:
- Possibilities of generalization for other spaces with some additional structures or dimensions.
- Applications in dynamical systems, other branches of mathematics and real life(!?)
Some references are appreciated.
dynamical-systems
edited Jul 21 at 1:55
David_Shmij
398116
asked Jul 21 at 0:49
C. Junior
637311
edited Jul 21 at 1:55
David_Shmij
398116
edited Jul 21 at 1:55
David_Shmij
398116
edited Jul 21 at 1:55
David_Shmij
398116
398116
asked Jul 21 at 0:49
C. Junior
637311
asked Jul 21 at 0:49
C. Junior
637311
asked Jul 21 at 0:49
C. Junior
637311
637311
closed as too broad by Did, Taroccoesbrocco, max_zorn, Jose Arnaldo Bebita Dris, Parcly Taxel Jul 22 at 13:33
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as too broad by Did, Taroccoesbrocco, max_zorn, Jose Arnaldo Bebita Dris, Parcly Taxel Jul 22 at 13:33
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
Could you please be a bit more specific as to what generalizations you are looking for? As to the applications, Sharkovskii's theorem is a result on periodicity of dynamical systems.
– David_Shmij
Jul 21 at 1:49
1
I would recommend you read the paper "Period Three Implies Chaos" by Tien-Yien Li & James A. Yorke
– David_Shmij
Jul 21 at 2:02
Just try Googling Sharkovskii theorem.
– user539887
Jul 21 at 8:59
4
Almost the same question was posted in MO References and background on Sharkovskii's theorem. I think that simultaneous cross-posting, without mentioning it, is considered a bad practice
– user539887
Jul 21 at 9:49
add a comment |Â
1
Could you please be a bit more specific as to what generalizations you are looking for? As to the applications, Sharkovskii's theorem is a result on periodicity of dynamical systems.
– David_Shmij
Jul 21 at 1:49
1
I would recommend you read the paper "Period Three Implies Chaos" by Tien-Yien Li & James A. Yorke
– David_Shmij
Jul 21 at 2:02
Just try Googling Sharkovskii theorem.
– user539887
Jul 21 at 8:59
4
Almost the same question was posted in MO References and background on Sharkovskii's theorem. I think that simultaneous cross-posting, without mentioning it, is considered a bad practice
– user539887
Jul 21 at 9:49
1
1
Could you please be a bit more specific as to what generalizations you are looking for? As to the applications, Sharkovskii's theorem is a result on periodicity of dynamical systems.
– David_Shmij
Jul 21 at 1:49
Could you please be a bit more specific as to what generalizations you are looking for? As to the applications, Sharkovskii's theorem is a result on periodicity of dynamical systems.
– David_Shmij
Jul 21 at 1:49
1
1
I would recommend you read the paper "Period Three Implies Chaos" by Tien-Yien Li & James A. Yorke
– David_Shmij
Jul 21 at 2:02
I would recommend you read the paper "Period Three Implies Chaos" by Tien-Yien Li & James A. Yorke
– David_Shmij
Jul 21 at 2:02
Just try Googling Sharkovskii theorem.
– user539887
Jul 21 at 8:59
Just try Googling Sharkovskii theorem.
– user539887
Jul 21 at 8:59
4
4
Almost the same question was posted in MO References and background on Sharkovskii's theorem. I think that simultaneous cross-posting, without mentioning it, is considered a bad practice
– user539887
Jul 21 at 9:49
Almost the same question was posted in MO References and background on Sharkovskii's theorem. I think that simultaneous cross-posting, without mentioning it, is considered a bad practice
– user539887
Jul 21 at 9:49
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
Just quickly, it is not true in the circle. It has been shown in the context of unique beta expansions. See N. Sidorov et al paper Periodic unique beta-expansions: the SharkovskiÄ ordering. Perhaps, it might hold on some one-dimensional spaces like finite graphs without circles or hereditarly indecomposable continua such as the pseudoarc. Seems difficult to hold for higher dimensional spaces in my opinion.
As for applications a quick one is related to the structure of some limit spaces of tent maps. Check W. Ingram's work.
answered Jul 21 at 20:43
Rafael Alcaraz Barrera
1618
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Just quickly, it is not true in the circle. It has been shown in the context of unique beta expansions. See N. Sidorov et al paper Periodic unique beta-expansions: the SharkovskiÄ ordering. Perhaps, it might hold on some one-dimensional spaces like finite graphs without circles or hereditarly indecomposable continua such as the pseudoarc. Seems difficult to hold for higher dimensional spaces in my opinion.
As for applications a quick one is related to the structure of some limit spaces of tent maps. Check W. Ingram's work.
answered Jul 21 at 20:43
Rafael Alcaraz Barrera
1618
add a comment |Â
up vote
1
down vote
accepted
Just quickly, it is not true in the circle. It has been shown in the context of unique beta expansions. See N. Sidorov et al paper Periodic unique beta-expansions: the SharkovskiÄ ordering. Perhaps, it might hold on some one-dimensional spaces like finite graphs without circles or hereditarly indecomposable continua such as the pseudoarc. Seems difficult to hold for higher dimensional spaces in my opinion.
As for applications a quick one is related to the structure of some limit spaces of tent maps. Check W. Ingram's work.
answered Jul 21 at 20:43
Rafael Alcaraz Barrera
1618
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Just quickly, it is not true in the circle. It has been shown in the context of unique beta expansions. See N. Sidorov et al paper Periodic unique beta-expansions: the SharkovskiÄ ordering. Perhaps, it might hold on some one-dimensional spaces like finite graphs without circles or hereditarly indecomposable continua such as the pseudoarc. Seems difficult to hold for higher dimensional spaces in my opinion.
As for applications a quick one is related to the structure of some limit spaces of tent maps. Check W. Ingram's work.
answered Jul 21 at 20:43
Rafael Alcaraz Barrera
1618
Just quickly, it is not true in the circle. It has been shown in the context of unique beta expansions. See N. Sidorov et al paper Periodic unique beta-expansions: the SharkovskiÄ ordering. Perhaps, it might hold on some one-dimensional spaces like finite graphs without circles or hereditarly indecomposable continua such as the pseudoarc. Seems difficult to hold for higher dimensional spaces in my opinion.
As for applications a quick one is related to the structure of some limit spaces of tent maps. Check W. Ingram's work.
answered Jul 21 at 20:43
Rafael Alcaraz Barrera
1618
answered Jul 21 at 20:43
Rafael Alcaraz Barrera
1618
answered Jul 21 at 20:43
Rafael Alcaraz Barrera
1618
answered Jul 21 at 20:43
Rafael Alcaraz Barrera
1618
1618
add a comment |Â
add a comment |Â
1
Could you please be a bit more specific as to what generalizations you are looking for? As to the applications, Sharkovskii's theorem is a result on periodicity of dynamical systems.
– David_Shmij
Jul 21 at 1:49
1
I would recommend you read the paper "Period Three Implies Chaos" by Tien-Yien Li & James A. Yorke
– David_Shmij
Jul 21 at 2:02
Just try Googling Sharkovskii theorem.
– user539887
Jul 21 at 8:59
4
Almost the same question was posted in MO References and background on Sharkovskii's theorem. I think that simultaneous cross-posting, without mentioning it, is considered a bad practice
– user539887
Jul 21 at 9:49